# data_list remains the same

    Code
      lapply(models, "[[", "data_list")
    Output
      $m0a
      $m0a$M_lvlone
          M1 (Intercept)
      1    1           1
      2    2           1
      3    2           1
      4    1           1
      5    3           1
      6    3           1
      7    3           1
      8    3           1
      9    1           1
      10   2           1
      11   1           1
      12   2           1
      13   1           1
      14   4           1
      15   2           1
      16   3           1
      17   3           1
      18   1           1
      19   2           1
      20   2           1
      21   1           1
      22   4           1
      23   1           1
      24   2           1
      25   1           1
      26   1           1
      27   2           1
      28   1           1
      29   3           1
      30   1           1
      31   4           1
      32   1           1
      33   4           1
      34   2           1
      35   1           1
      36   1           1
      37   1           1
      38   2           1
      39   2           1
      40   2           1
      41   4           1
      42   4           1
      43   4           1
      44   4           1
      45   2           1
      46   1           1
      47   3           1
      48   3           1
      49   2           1
      50   2           1
      51   3           1
      52   1           1
      53   2           1
      54   3           1
      55   2           1
      56   1           1
      57   4           1
      58   1           1
      59   4           1
      60   1           1
      61   1           1
      62   1           1
      63   4           1
      64   1           1
      65   2           1
      66   4           1
      67   4           1
      68   3           1
      69   3           1
      70   2           1
      71   3           1
      72   2           1
      73   4           1
      74   2           1
      75   1           1
      76   3           1
      77   2           1
      78   4           1
      79   4           1
      80   1           1
      81   1           1
      82   4           1
      83   3           1
      84   4           1
      85   2           1
      86   4           1
      87   3           1
      88   3           1
      89   3           1
      90   1           1
      91   1           1
      92   1           1
      93   1           1
      94   3           1
      95   2           1
      96   1           1
      97   3           1
      98   4           1
      99   2           1
      100  1           1
      
      $m0a$mu_reg_multinomial
      [1] 0
      
      $m0a$tau_reg_multinomial
      [1] 1e-04
      
      
      $m0b
      $m0b$M_lvlone
          M2 (Intercept)
      1    4           1
      2    1           1
      3    3           1
      4    3           1
      5    4           1
      6    4           1
      7    1           1
      8    1           1
      9    2           1
      10   2           1
      11   3           1
      12   3           1
      13   2           1
      14   3           1
      15   2           1
      16   1           1
      17   4           1
      18   2           1
      19   3           1
      20   3           1
      21   2           1
      22   2           1
      23   3           1
      24   3           1
      25   2           1
      26   2           1
      27   1           1
      28   3           1
      29   4           1
      30   2           1
      31  NA           1
      32   4           1
      33   4           1
      34   4           1
      35   2           1
      36   1           1
      37   3           1
      38   4           1
      39   3           1
      40   3           1
      41   1           1
      42   4           1
      43   1           1
      44   2           1
      45   2           1
      46   1           1
      47   4           1
      48   2           1
      49   4           1
      50   1           1
      51   4           1
      52   4           1
      53   4           1
      54   3           1
      55   3           1
      56   3           1
      57   2           1
      58   3           1
      59   3           1
      60   4           1
      61   2           1
      62   2           1
      63   1           1
      64   2           1
      65   2           1
      66   3           1
      67   2           1
      68   4           1
      69  NA           1
      70   1           1
      71   2           1
      72   3           1
      73   4           1
      74   4           1
      75   1           1
      76   4           1
      77  NA           1
      78   2           1
      79   2           1
      80   2           1
      81   4           1
      82   3           1
      83   3           1
      84   1           1
      85   2           1
      86   1           1
      87   3           1
      88   1           1
      89   2           1
      90   1           1
      91   3           1
      92   1           1
      93   4           1
      94   4           1
      95   1           1
      96   4           1
      97   4           1
      98   3           1
      99   3           1
      100  4           1
      
      $m0b$mu_reg_multinomial
      [1] 0
      
      $m0b$tau_reg_multinomial
      [1] 1e-04
      
      
      $m1a
      $m1a$M_lvlone
          M1 (Intercept)       C1
      1    1           1 1.410531
      2    2           1 1.434183
      3    2           1 1.430994
      4    1           1 1.453096
      5    3           1 1.438344
      6    3           1 1.453207
      7    3           1 1.425176
      8    3           1 1.437908
      9    1           1 1.416911
      10   2           1 1.448638
      11   1           1 1.428375
      12   2           1 1.450130
      13   1           1 1.420545
      14   4           1 1.423005
      15   2           1 1.435902
      16   3           1 1.423901
      17   3           1 1.457208
      18   1           1 1.414280
      19   2           1 1.443383
      20   2           1 1.434954
      21   1           1 1.429499
      22   4           1 1.441897
      23   1           1 1.423713
      24   2           1 1.435395
      25   1           1 1.425944
      26   1           1 1.437115
      27   2           1 1.441326
      28   1           1 1.422953
      29   3           1 1.437797
      30   1           1 1.472121
      31   4           1 1.421782
      32   1           1 1.457672
      33   4           1 1.430842
      34   2           1 1.431523
      35   1           1 1.421395
      36   1           1 1.434496
      37   1           1 1.425383
      38   2           1 1.421802
      39   2           1 1.430094
      40   2           1 1.447621
      41   4           1 1.434797
      42   4           1 1.446091
      43   4           1 1.445306
      44   4           1 1.448783
      45   2           1 1.450617
      46   1           1 1.415055
      47   3           1 1.436590
      48   3           1 1.433938
      49   2           1 1.414941
      50   2           1 1.421807
      51   3           1 1.453203
      52   1           1 1.452129
      53   2           1 1.431510
      54   3           1 1.430082
      55   2           1 1.443492
      56   1           1 1.436460
      57   4           1 1.418119
      58   1           1 1.434971
      59   4           1 1.445599
      60   1           1 1.437097
      61   1           1 1.428360
      62   1           1 1.440550
      63   4           1 1.443014
      64   1           1 1.424298
      65   2           1 1.448823
      66   4           1 1.425834
      67   4           1 1.427102
      68   3           1 1.414240
      69   3           1 1.456218
      70   2           1 1.470594
      71   3           1 1.425058
      72   2           1 1.432371
      73   4           1 1.441656
      74   2           1 1.434952
      75   1           1 1.402860
      76   3           1 1.453363
      77   2           1 1.432909
      78   4           1 1.435103
      79   4           1 1.434462
      80   1           1 1.434661
      81   1           1 1.445881
      82   4           1 1.442548
      83   3           1 1.430097
      84   4           1 1.430119
      85   2           1 1.430315
      86   4           1 1.437584
      87   3           1 1.409738
      88   3           1 1.422388
      89   3           1 1.422509
      90   1           1 1.439432
      91   1           1 1.430175
      92   1           1 1.418002
      93   1           1 1.423812
      94   3           1 1.423473
      95   2           1 1.434412
      96   1           1 1.450844
      97   3           1 1.433371
      98   4           1 1.444378
      99   2           1 1.422523
      100  1           1 1.410394
      
      $m1a$spM_lvlone
                    center      scale
      M1                NA         NA
      (Intercept)       NA         NA
      C1          1.434101 0.01299651
      
      $m1a$mu_reg_multinomial
      [1] 0
      
      $m1a$tau_reg_multinomial
      [1] 1e-04
      
      
      $m1b
      $m1b$M_lvlone
          M2 (Intercept)       C1
      1    4           1 1.410531
      2    1           1 1.434183
      3    3           1 1.430994
      4    3           1 1.453096
      5    4           1 1.438344
      6    4           1 1.453207
      7    1           1 1.425176
      8    1           1 1.437908
      9    2           1 1.416911
      10   2           1 1.448638
      11   3           1 1.428375
      12   3           1 1.450130
      13   2           1 1.420545
      14   3           1 1.423005
      15   2           1 1.435902
      16   1           1 1.423901
      17   4           1 1.457208
      18   2           1 1.414280
      19   3           1 1.443383
      20   3           1 1.434954
      21   2           1 1.429499
      22   2           1 1.441897
      23   3           1 1.423713
      24   3           1 1.435395
      25   2           1 1.425944
      26   2           1 1.437115
      27   1           1 1.441326
      28   3           1 1.422953
      29   4           1 1.437797
      30   2           1 1.472121
      31  NA           1 1.421782
      32   4           1 1.457672
      33   4           1 1.430842
      34   4           1 1.431523
      35   2           1 1.421395
      36   1           1 1.434496
      37   3           1 1.425383
      38   4           1 1.421802
      39   3           1 1.430094
      40   3           1 1.447621
      41   1           1 1.434797
      42   4           1 1.446091
      43   1           1 1.445306
      44   2           1 1.448783
      45   2           1 1.450617
      46   1           1 1.415055
      47   4           1 1.436590
      48   2           1 1.433938
      49   4           1 1.414941
      50   1           1 1.421807
      51   4           1 1.453203
      52   4           1 1.452129
      53   4           1 1.431510
      54   3           1 1.430082
      55   3           1 1.443492
      56   3           1 1.436460
      57   2           1 1.418119
      58   3           1 1.434971
      59   3           1 1.445599
      60   4           1 1.437097
      61   2           1 1.428360
      62   2           1 1.440550
      63   1           1 1.443014
      64   2           1 1.424298
      65   2           1 1.448823
      66   3           1 1.425834
      67   2           1 1.427102
      68   4           1 1.414240
      69  NA           1 1.456218
      70   1           1 1.470594
      71   2           1 1.425058
      72   3           1 1.432371
      73   4           1 1.441656
      74   4           1 1.434952
      75   1           1 1.402860
      76   4           1 1.453363
      77  NA           1 1.432909
      78   2           1 1.435103
      79   2           1 1.434462
      80   2           1 1.434661
      81   4           1 1.445881
      82   3           1 1.442548
      83   3           1 1.430097
      84   1           1 1.430119
      85   2           1 1.430315
      86   1           1 1.437584
      87   3           1 1.409738
      88   1           1 1.422388
      89   2           1 1.422509
      90   1           1 1.439432
      91   3           1 1.430175
      92   1           1 1.418002
      93   4           1 1.423812
      94   4           1 1.423473
      95   1           1 1.434412
      96   4           1 1.450844
      97   4           1 1.433371
      98   3           1 1.444378
      99   3           1 1.422523
      100  4           1 1.410394
      
      $m1b$spM_lvlone
                    center      scale
      M2                NA         NA
      (Intercept)       NA         NA
      C1          1.434101 0.01299651
      
      $m1b$mu_reg_multinomial
      [1] 0
      
      $m1b$tau_reg_multinomial
      [1] 1e-04
      
      
      $m2a
      $m2a$M_lvlone
          M1           C2 (Intercept)
      1    1  0.144065882           1
      2    2  0.032778478           1
      3    2  0.343008492           1
      4    1 -0.361887858           1
      5    3 -0.389600647           1
      6    3 -0.205306841           1
      7    3  0.079434830           1
      8    3 -0.331246757           1
      9    1 -0.329638800           1
      10   2  0.167597533           1
      11   1  0.860207989           1
      12   2  0.022730640           1
      13   1  0.217171172           1
      14   4 -0.403002412           1
      15   2  0.087369742           1
      16   3 -0.183870429           1
      17   3 -0.194577002           1
      18   1 -0.349718516           1
      19   2 -0.508781244           1
      20   2  0.494883111           1
      21   1  0.258041067           1
      22   4 -0.922621989           1
      23   1  0.431254949           1
      24   2 -0.294218881           1
      25   1 -0.425548895           1
      26   1  0.057176054           1
      27   2  0.289090158           1
      28   1 -0.473079489           1
      29   3 -0.385664863           1
      30   1 -0.154780107           1
      31   4  0.100536296           1
      32   1  0.634791958           1
      33   4 -0.387252617           1
      34   2 -0.181741088           1
      35   1 -0.311562695           1
      36   1 -0.044115907           1
      37   1 -0.657409991           1
      38   2  0.159577214           1
      39   2 -0.460416933           1
      40   2           NA           1
      41   4 -0.248909867           1
      42   4 -0.609021545           1
      43   4  0.025471883           1
      44   4  0.066648592           1
      45   2 -0.276108719           1
      46   1 -0.179737577           1
      47   3  0.181190937           1
      48   3 -0.453871693           1
      49   2  0.448629602           1
      50   2 -0.529811821           1
      51   3 -0.028304571           1
      52   1 -0.520318482           1
      53   2  0.171317619           1
      54   3  0.432732046           1
      55   2 -0.346286005           1
      56   1 -0.469375653           1
      57   4  0.031021711           1
      58   1 -0.118837515           1
      59   4  0.507769984           1
      60   1  0.271797031           1
      61   1 -0.124442204           1
      62   1  0.277677389           1
      63   4 -0.102893730           1
      64   1           NA           1
      65   2 -0.678303052           1
      66   4  0.478880037           1
      67   4 -0.428028760           1
      68   3  0.048119185           1
      69   3  0.216932805           1
      70   2 -0.234575269           1
      71   3  0.006827078           1
      72   2 -0.456055171           1
      73   4  0.346486708           1
      74   2  0.205092215           1
      75   1 -0.136596858           1
      76   3 -0.500179043           1
      77   2  0.527352086           1
      78   4  0.022742250           1
      79   4           NA           1
      80   1 -0.002032440           1
      81   1 -0.154246160           1
      82   4  0.140201825           1
      83   3 -0.141417121           1
      84   4           NA           1
      85   2 -0.021285339           1
      86   4 -0.010196306           1
      87   3 -0.089747520           1
      88   3 -0.083699898           1
      89   3 -0.044061996           1
      90   1 -0.209291697           1
      91   1  0.639036426           1
      92   1  0.094698299           1
      93   1 -0.055510622           1
      94   3 -0.421318463           1
      95   2  0.125295503           1
      96   1  0.213084904           1
      97   3 -0.161914659           1
      98   4 -0.034767685           1
      99   2 -0.320681689           1
      100  1  0.058192962           1
      
      $m2a$spM_lvlone
                       center     scale
      M1                   NA        NA
      C2          -0.06490582 0.3331735
      (Intercept)          NA        NA
      
      $m2a$mu_reg_norm
      [1] 0
      
      $m2a$tau_reg_norm
      [1] 1e-04
      
      $m2a$shape_tau_norm
      [1] 0.01
      
      $m2a$rate_tau_norm
      [1] 0.01
      
      $m2a$mu_reg_multinomial
      [1] 0
      
      $m2a$tau_reg_multinomial
      [1] 1e-04
      
      
      $m2b
      $m2b$M_lvlone
          M2           C2 (Intercept)
      1    4  0.144065882           1
      2    1  0.032778478           1
      3    3  0.343008492           1
      4    3 -0.361887858           1
      5    4 -0.389600647           1
      6    4 -0.205306841           1
      7    1  0.079434830           1
      8    1 -0.331246757           1
      9    2 -0.329638800           1
      10   2  0.167597533           1
      11   3  0.860207989           1
      12   3  0.022730640           1
      13   2  0.217171172           1
      14   3 -0.403002412           1
      15   2  0.087369742           1
      16   1 -0.183870429           1
      17   4 -0.194577002           1
      18   2 -0.349718516           1
      19   3 -0.508781244           1
      20   3  0.494883111           1
      21   2  0.258041067           1
      22   2 -0.922621989           1
      23   3  0.431254949           1
      24   3 -0.294218881           1
      25   2 -0.425548895           1
      26   2  0.057176054           1
      27   1  0.289090158           1
      28   3 -0.473079489           1
      29   4 -0.385664863           1
      30   2 -0.154780107           1
      31  NA  0.100536296           1
      32   4  0.634791958           1
      33   4 -0.387252617           1
      34   4 -0.181741088           1
      35   2 -0.311562695           1
      36   1 -0.044115907           1
      37   3 -0.657409991           1
      38   4  0.159577214           1
      39   3 -0.460416933           1
      40   3           NA           1
      41   1 -0.248909867           1
      42   4 -0.609021545           1
      43   1  0.025471883           1
      44   2  0.066648592           1
      45   2 -0.276108719           1
      46   1 -0.179737577           1
      47   4  0.181190937           1
      48   2 -0.453871693           1
      49   4  0.448629602           1
      50   1 -0.529811821           1
      51   4 -0.028304571           1
      52   4 -0.520318482           1
      53   4  0.171317619           1
      54   3  0.432732046           1
      55   3 -0.346286005           1
      56   3 -0.469375653           1
      57   2  0.031021711           1
      58   3 -0.118837515           1
      59   3  0.507769984           1
      60   4  0.271797031           1
      61   2 -0.124442204           1
      62   2  0.277677389           1
      63   1 -0.102893730           1
      64   2           NA           1
      65   2 -0.678303052           1
      66   3  0.478880037           1
      67   2 -0.428028760           1
      68   4  0.048119185           1
      69  NA  0.216932805           1
      70   1 -0.234575269           1
      71   2  0.006827078           1
      72   3 -0.456055171           1
      73   4  0.346486708           1
      74   4  0.205092215           1
      75   1 -0.136596858           1
      76   4 -0.500179043           1
      77  NA  0.527352086           1
      78   2  0.022742250           1
      79   2           NA           1
      80   2 -0.002032440           1
      81   4 -0.154246160           1
      82   3  0.140201825           1
      83   3 -0.141417121           1
      84   1           NA           1
      85   2 -0.021285339           1
      86   1 -0.010196306           1
      87   3 -0.089747520           1
      88   1 -0.083699898           1
      89   2 -0.044061996           1
      90   1 -0.209291697           1
      91   3  0.639036426           1
      92   1  0.094698299           1
      93   4 -0.055510622           1
      94   4 -0.421318463           1
      95   1  0.125295503           1
      96   4  0.213084904           1
      97   4 -0.161914659           1
      98   3 -0.034767685           1
      99   3 -0.320681689           1
      100  4  0.058192962           1
      
      $m2b$spM_lvlone
                       center     scale
      M2                   NA        NA
      C2          -0.06490582 0.3331735
      (Intercept)          NA        NA
      
      $m2b$mu_reg_norm
      [1] 0
      
      $m2b$tau_reg_norm
      [1] 1e-04
      
      $m2b$shape_tau_norm
      [1] 0.01
      
      $m2b$rate_tau_norm
      [1] 0.01
      
      $m2b$mu_reg_multinomial
      [1] 0
      
      $m2b$tau_reg_multinomial
      [1] 1e-04
      
      
      $m3a
      $m3a$M_lvlone
                C1 (Intercept) M12 M13 M14
      1   1.410531           1   0   0   0
      2   1.434183           1   1   0   0
      3   1.430994           1   1   0   0
      4   1.453096           1   0   0   0
      5   1.438344           1   0   1   0
      6   1.453207           1   0   1   0
      7   1.425176           1   0   1   0
      8   1.437908           1   0   1   0
      9   1.416911           1   0   0   0
      10  1.448638           1   1   0   0
      11  1.428375           1   0   0   0
      12  1.450130           1   1   0   0
      13  1.420545           1   0   0   0
      14  1.423005           1   0   0   1
      15  1.435902           1   1   0   0
      16  1.423901           1   0   1   0
      17  1.457208           1   0   1   0
      18  1.414280           1   0   0   0
      19  1.443383           1   1   0   0
      20  1.434954           1   1   0   0
      21  1.429499           1   0   0   0
      22  1.441897           1   0   0   1
      23  1.423713           1   0   0   0
      24  1.435395           1   1   0   0
      25  1.425944           1   0   0   0
      26  1.437115           1   0   0   0
      27  1.441326           1   1   0   0
      28  1.422953           1   0   0   0
      29  1.437797           1   0   1   0
      30  1.472121           1   0   0   0
      31  1.421782           1   0   0   1
      32  1.457672           1   0   0   0
      33  1.430842           1   0   0   1
      34  1.431523           1   1   0   0
      35  1.421395           1   0   0   0
      36  1.434496           1   0   0   0
      37  1.425383           1   0   0   0
      38  1.421802           1   1   0   0
      39  1.430094           1   1   0   0
      40  1.447621           1   1   0   0
      41  1.434797           1   0   0   1
      42  1.446091           1   0   0   1
      43  1.445306           1   0   0   1
      44  1.448783           1   0   0   1
      45  1.450617           1   1   0   0
      46  1.415055           1   0   0   0
      47  1.436590           1   0   1   0
      48  1.433938           1   0   1   0
      49  1.414941           1   1   0   0
      50  1.421807           1   1   0   0
      51  1.453203           1   0   1   0
      52  1.452129           1   0   0   0
      53  1.431510           1   1   0   0
      54  1.430082           1   0   1   0
      55  1.443492           1   1   0   0
      56  1.436460           1   0   0   0
      57  1.418119           1   0   0   1
      58  1.434971           1   0   0   0
      59  1.445599           1   0   0   1
      60  1.437097           1   0   0   0
      61  1.428360           1   0   0   0
      62  1.440550           1   0   0   0
      63  1.443014           1   0   0   1
      64  1.424298           1   0   0   0
      65  1.448823           1   1   0   0
      66  1.425834           1   0   0   1
      67  1.427102           1   0   0   1
      68  1.414240           1   0   1   0
      69  1.456218           1   0   1   0
      70  1.470594           1   1   0   0
      71  1.425058           1   0   1   0
      72  1.432371           1   1   0   0
      73  1.441656           1   0   0   1
      74  1.434952           1   1   0   0
      75  1.402860           1   0   0   0
      76  1.453363           1   0   1   0
      77  1.432909           1   1   0   0
      78  1.435103           1   0   0   1
      79  1.434462           1   0   0   1
      80  1.434661           1   0   0   0
      81  1.445881           1   0   0   0
      82  1.442548           1   0   0   1
      83  1.430097           1   0   1   0
      84  1.430119           1   0   0   1
      85  1.430315           1   1   0   0
      86  1.437584           1   0   0   1
      87  1.409738           1   0   1   0
      88  1.422388           1   0   1   0
      89  1.422509           1   0   1   0
      90  1.439432           1   0   0   0
      91  1.430175           1   0   0   0
      92  1.418002           1   0   0   0
      93  1.423812           1   0   0   0
      94  1.423473           1   0   1   0
      95  1.434412           1   1   0   0
      96  1.450844           1   0   0   0
      97  1.433371           1   0   1   0
      98  1.444378           1   0   0   1
      99  1.422523           1   1   0   0
      100 1.410394           1   0   0   0
      
      $m3a$mu_reg_norm
      [1] 0
      
      $m3a$tau_reg_norm
      [1] 1e-04
      
      $m3a$shape_tau_norm
      [1] 0.01
      
      $m3a$rate_tau_norm
      [1] 0.01
      
      
      $m3b
      $m3b$M_lvlone
                C1 M2 (Intercept) M22 M23 M24
      1   1.410531  4           1  NA  NA  NA
      2   1.434183  1           1  NA  NA  NA
      3   1.430994  3           1  NA  NA  NA
      4   1.453096  3           1  NA  NA  NA
      5   1.438344  4           1  NA  NA  NA
      6   1.453207  4           1  NA  NA  NA
      7   1.425176  1           1  NA  NA  NA
      8   1.437908  1           1  NA  NA  NA
      9   1.416911  2           1  NA  NA  NA
      10  1.448638  2           1  NA  NA  NA
      11  1.428375  3           1  NA  NA  NA
      12  1.450130  3           1  NA  NA  NA
      13  1.420545  2           1  NA  NA  NA
      14  1.423005  3           1  NA  NA  NA
      15  1.435902  2           1  NA  NA  NA
      16  1.423901  1           1  NA  NA  NA
      17  1.457208  4           1  NA  NA  NA
      18  1.414280  2           1  NA  NA  NA
      19  1.443383  3           1  NA  NA  NA
      20  1.434954  3           1  NA  NA  NA
      21  1.429499  2           1  NA  NA  NA
      22  1.441897  2           1  NA  NA  NA
      23  1.423713  3           1  NA  NA  NA
      24  1.435395  3           1  NA  NA  NA
      25  1.425944  2           1  NA  NA  NA
      26  1.437115  2           1  NA  NA  NA
      27  1.441326  1           1  NA  NA  NA
      28  1.422953  3           1  NA  NA  NA
      29  1.437797  4           1  NA  NA  NA
      30  1.472121  2           1  NA  NA  NA
      31  1.421782 NA           1  NA  NA  NA
      32  1.457672  4           1  NA  NA  NA
      33  1.430842  4           1  NA  NA  NA
      34  1.431523  4           1  NA  NA  NA
      35  1.421395  2           1  NA  NA  NA
      36  1.434496  1           1  NA  NA  NA
      37  1.425383  3           1  NA  NA  NA
      38  1.421802  4           1  NA  NA  NA
      39  1.430094  3           1  NA  NA  NA
      40  1.447621  3           1  NA  NA  NA
      41  1.434797  1           1  NA  NA  NA
      42  1.446091  4           1  NA  NA  NA
      43  1.445306  1           1  NA  NA  NA
      44  1.448783  2           1  NA  NA  NA
      45  1.450617  2           1  NA  NA  NA
      46  1.415055  1           1  NA  NA  NA
      47  1.436590  4           1  NA  NA  NA
      48  1.433938  2           1  NA  NA  NA
      49  1.414941  4           1  NA  NA  NA
      50  1.421807  1           1  NA  NA  NA
      51  1.453203  4           1  NA  NA  NA
      52  1.452129  4           1  NA  NA  NA
      53  1.431510  4           1  NA  NA  NA
      54  1.430082  3           1  NA  NA  NA
      55  1.443492  3           1  NA  NA  NA
      56  1.436460  3           1  NA  NA  NA
      57  1.418119  2           1  NA  NA  NA
      58  1.434971  3           1  NA  NA  NA
      59  1.445599  3           1  NA  NA  NA
      60  1.437097  4           1  NA  NA  NA
      61  1.428360  2           1  NA  NA  NA
      62  1.440550  2           1  NA  NA  NA
      63  1.443014  1           1  NA  NA  NA
      64  1.424298  2           1  NA  NA  NA
      65  1.448823  2           1  NA  NA  NA
      66  1.425834  3           1  NA  NA  NA
      67  1.427102  2           1  NA  NA  NA
      68  1.414240  4           1  NA  NA  NA
      69  1.456218 NA           1  NA  NA  NA
      70  1.470594  1           1  NA  NA  NA
      71  1.425058  2           1  NA  NA  NA
      72  1.432371  3           1  NA  NA  NA
      73  1.441656  4           1  NA  NA  NA
      74  1.434952  4           1  NA  NA  NA
      75  1.402860  1           1  NA  NA  NA
      76  1.453363  4           1  NA  NA  NA
      77  1.432909 NA           1  NA  NA  NA
      78  1.435103  2           1  NA  NA  NA
      79  1.434462  2           1  NA  NA  NA
      80  1.434661  2           1  NA  NA  NA
      81  1.445881  4           1  NA  NA  NA
      82  1.442548  3           1  NA  NA  NA
      83  1.430097  3           1  NA  NA  NA
      84  1.430119  1           1  NA  NA  NA
      85  1.430315  2           1  NA  NA  NA
      86  1.437584  1           1  NA  NA  NA
      87  1.409738  3           1  NA  NA  NA
      88  1.422388  1           1  NA  NA  NA
      89  1.422509  2           1  NA  NA  NA
      90  1.439432  1           1  NA  NA  NA
      91  1.430175  3           1  NA  NA  NA
      92  1.418002  1           1  NA  NA  NA
      93  1.423812  4           1  NA  NA  NA
      94  1.423473  4           1  NA  NA  NA
      95  1.434412  1           1  NA  NA  NA
      96  1.450844  4           1  NA  NA  NA
      97  1.433371  4           1  NA  NA  NA
      98  1.444378  3           1  NA  NA  NA
      99  1.422523  3           1  NA  NA  NA
      100 1.410394  4           1  NA  NA  NA
      
      $m3b$mu_reg_norm
      [1] 0
      
      $m3b$tau_reg_norm
      [1] 1e-04
      
      $m3b$shape_tau_norm
      [1] 0.01
      
      $m3b$rate_tau_norm
      [1] 0.01
      
      $m3b$mu_reg_multinomial
      [1] 0
      
      $m3b$tau_reg_multinomial
      [1] 1e-04
      
      
      $m4a
      $m4a$M_lvlone
          M1           C2 M2 O2 (Intercept) M22 M23 M24 O22 O23 O24 abs(C1 - C2)
      1    1  0.144065882  4  4           1  NA  NA  NA  NA  NA  NA           NA
      2    2  0.032778478  1  4           1  NA  NA  NA  NA  NA  NA           NA
      3    2  0.343008492  3  4           1  NA  NA  NA  NA  NA  NA           NA
      4    1 -0.361887858  3  1           1  NA  NA  NA  NA  NA  NA           NA
      5    3 -0.389600647  4  2           1  NA  NA  NA  NA  NA  NA           NA
      6    3 -0.205306841  4  3           1  NA  NA  NA  NA  NA  NA           NA
      7    3  0.079434830  1  4           1  NA  NA  NA  NA  NA  NA           NA
      8    3 -0.331246757  1  2           1  NA  NA  NA  NA  NA  NA           NA
      9    1 -0.329638800  2  4           1  NA  NA  NA  NA  NA  NA           NA
      10   2  0.167597533  2  3           1  NA  NA  NA  NA  NA  NA           NA
      11   1  0.860207989  3  2           1  NA  NA  NA  NA  NA  NA           NA
      12   2  0.022730640  3  1           1  NA  NA  NA  NA  NA  NA           NA
      13   1  0.217171172  2  1           1  NA  NA  NA  NA  NA  NA           NA
      14   4 -0.403002412  3  1           1  NA  NA  NA  NA  NA  NA           NA
      15   2  0.087369742  2  4           1  NA  NA  NA  NA  NA  NA           NA
      16   3 -0.183870429  1  3           1  NA  NA  NA  NA  NA  NA           NA
      17   3 -0.194577002  4  3           1  NA  NA  NA  NA  NA  NA           NA
      18   1 -0.349718516  2  1           1  NA  NA  NA  NA  NA  NA           NA
      19   2 -0.508781244  3  3           1  NA  NA  NA  NA  NA  NA           NA
      20   2  0.494883111  3  1           1  NA  NA  NA  NA  NA  NA           NA
      21   1  0.258041067  2  3           1  NA  NA  NA  NA  NA  NA           NA
      22   4 -0.922621989  2  3           1  NA  NA  NA  NA  NA  NA           NA
      23   1  0.431254949  3  2           1  NA  NA  NA  NA  NA  NA           NA
      24   2 -0.294218881  3  3           1  NA  NA  NA  NA  NA  NA           NA
      25   1 -0.425548895  2  2           1  NA  NA  NA  NA  NA  NA           NA
      26   1  0.057176054  2  2           1  NA  NA  NA  NA  NA  NA           NA
      27   2  0.289090158  1  1           1  NA  NA  NA  NA  NA  NA           NA
      28   1 -0.473079489  3  4           1  NA  NA  NA  NA  NA  NA           NA
      29   3 -0.385664863  4  3           1  NA  NA  NA  NA  NA  NA           NA
      30   1 -0.154780107  2  3           1  NA  NA  NA  NA  NA  NA           NA
      31   4  0.100536296 NA  2           1  NA  NA  NA  NA  NA  NA           NA
      32   1  0.634791958  4  2           1  NA  NA  NA  NA  NA  NA           NA
      33   4 -0.387252617  4  1           1  NA  NA  NA  NA  NA  NA           NA
      34   2 -0.181741088  4  1           1  NA  NA  NA  NA  NA  NA           NA
      35   1 -0.311562695  2  4           1  NA  NA  NA  NA  NA  NA           NA
      36   1 -0.044115907  1  3           1  NA  NA  NA  NA  NA  NA           NA
      37   1 -0.657409991  3  3           1  NA  NA  NA  NA  NA  NA           NA
      38   2  0.159577214  4  1           1  NA  NA  NA  NA  NA  NA           NA
      39   2 -0.460416933  3  2           1  NA  NA  NA  NA  NA  NA           NA
      40   2           NA  3  3           1  NA  NA  NA  NA  NA  NA           NA
      41   4 -0.248909867  1  3           1  NA  NA  NA  NA  NA  NA           NA
      42   4 -0.609021545  4  3           1  NA  NA  NA  NA  NA  NA           NA
      43   4  0.025471883  1  3           1  NA  NA  NA  NA  NA  NA           NA
      44   4  0.066648592  2  4           1  NA  NA  NA  NA  NA  NA           NA
      45   2 -0.276108719  2  4           1  NA  NA  NA  NA  NA  NA           NA
      46   1 -0.179737577  1  1           1  NA  NA  NA  NA  NA  NA           NA
      47   3  0.181190937  4  4           1  NA  NA  NA  NA  NA  NA           NA
      48   3 -0.453871693  2  4           1  NA  NA  NA  NA  NA  NA           NA
      49   2  0.448629602  4  1           1  NA  NA  NA  NA  NA  NA           NA
      50   2 -0.529811821  1  2           1  NA  NA  NA  NA  NA  NA           NA
      51   3 -0.028304571  4  1           1  NA  NA  NA  NA  NA  NA           NA
      52   1 -0.520318482  4  3           1  NA  NA  NA  NA  NA  NA           NA
      53   2  0.171317619  4  2           1  NA  NA  NA  NA  NA  NA           NA
      54   3  0.432732046  3  1           1  NA  NA  NA  NA  NA  NA           NA
      55   2 -0.346286005  3  2           1  NA  NA  NA  NA  NA  NA           NA
      56   1 -0.469375653  3  3           1  NA  NA  NA  NA  NA  NA           NA
      57   4  0.031021711  2 NA           1  NA  NA  NA  NA  NA  NA           NA
      58   1 -0.118837515  3  4           1  NA  NA  NA  NA  NA  NA           NA
      59   4  0.507769984  3  4           1  NA  NA  NA  NA  NA  NA           NA
      60   1  0.271797031  4  3           1  NA  NA  NA  NA  NA  NA           NA
      61   1 -0.124442204  2  4           1  NA  NA  NA  NA  NA  NA           NA
      62   1  0.277677389  2  1           1  NA  NA  NA  NA  NA  NA           NA
      63   4 -0.102893730  1  4           1  NA  NA  NA  NA  NA  NA           NA
      64   1           NA  2  4           1  NA  NA  NA  NA  NA  NA           NA
      65   2 -0.678303052  2  4           1  NA  NA  NA  NA  NA  NA           NA
      66   4  0.478880037  3  1           1  NA  NA  NA  NA  NA  NA           NA
      67   4 -0.428028760  2  3           1  NA  NA  NA  NA  NA  NA           NA
      68   3  0.048119185  4  3           1  NA  NA  NA  NA  NA  NA           NA
      69   3  0.216932805 NA  4           1  NA  NA  NA  NA  NA  NA           NA
      70   2 -0.234575269  1  1           1  NA  NA  NA  NA  NA  NA           NA
      71   3  0.006827078  2  4           1  NA  NA  NA  NA  NA  NA           NA
      72   2 -0.456055171  3  4           1  NA  NA  NA  NA  NA  NA           NA
      73   4  0.346486708  4  2           1  NA  NA  NA  NA  NA  NA           NA
      74   2  0.205092215  4  4           1  NA  NA  NA  NA  NA  NA           NA
      75   1 -0.136596858  1  3           1  NA  NA  NA  NA  NA  NA           NA
      76   3 -0.500179043  4  2           1  NA  NA  NA  NA  NA  NA           NA
      77   2  0.527352086 NA  2           1  NA  NA  NA  NA  NA  NA           NA
      78   4  0.022742250  2  3           1  NA  NA  NA  NA  NA  NA           NA
      79   4           NA  2  2           1  NA  NA  NA  NA  NA  NA           NA
      80   1 -0.002032440  2  1           1  NA  NA  NA  NA  NA  NA           NA
      81   1 -0.154246160  4  4           1  NA  NA  NA  NA  NA  NA           NA
      82   4  0.140201825  3  2           1  NA  NA  NA  NA  NA  NA           NA
      83   3 -0.141417121  3  4           1  NA  NA  NA  NA  NA  NA           NA
      84   4           NA  1  1           1  NA  NA  NA  NA  NA  NA           NA
      85   2 -0.021285339  2  1           1  NA  NA  NA  NA  NA  NA           NA
      86   4 -0.010196306  1  2           1  NA  NA  NA  NA  NA  NA           NA
      87   3 -0.089747520  3  3           1  NA  NA  NA  NA  NA  NA           NA
      88   3 -0.083699898  1  3           1  NA  NA  NA  NA  NA  NA           NA
      89   3 -0.044061996  2  2           1  NA  NA  NA  NA  NA  NA           NA
      90   1 -0.209291697  1  4           1  NA  NA  NA  NA  NA  NA           NA
      91   1  0.639036426  3  2           1  NA  NA  NA  NA  NA  NA           NA
      92   1  0.094698299  1  1           1  NA  NA  NA  NA  NA  NA           NA
      93   1 -0.055510622  4 NA           1  NA  NA  NA  NA  NA  NA           NA
      94   3 -0.421318463  4  3           1  NA  NA  NA  NA  NA  NA           NA
      95   2  0.125295503  1  1           1  NA  NA  NA  NA  NA  NA           NA
      96   1  0.213084904  4  3           1  NA  NA  NA  NA  NA  NA           NA
      97   3 -0.161914659  4  2           1  NA  NA  NA  NA  NA  NA           NA
      98   4 -0.034767685  3  2           1  NA  NA  NA  NA  NA  NA           NA
      99   2 -0.320681689  3  4           1  NA  NA  NA  NA  NA  NA           NA
      100  1  0.058192962  4  3           1  NA  NA  NA  NA  NA  NA           NA
            log(C1) O22:abs(C1 - C2) O23:abs(C1 - C2) O24:abs(C1 - C2)       C1
      1   0.3439662               NA               NA               NA 1.410531
      2   0.3605954               NA               NA               NA 1.434183
      3   0.3583696               NA               NA               NA 1.430994
      4   0.3736964               NA               NA               NA 1.453096
      5   0.3634928               NA               NA               NA 1.438344
      6   0.3737730               NA               NA               NA 1.453207
      7   0.3542952               NA               NA               NA 1.425176
      8   0.3631892               NA               NA               NA 1.437908
      9   0.3484794               NA               NA               NA 1.416911
      10  0.3706241               NA               NA               NA 1.448638
      11  0.3565373               NA               NA               NA 1.428375
      12  0.3716534               NA               NA               NA 1.450130
      13  0.3510408               NA               NA               NA 1.420545
      14  0.3527707               NA               NA               NA 1.423005
      15  0.3617934               NA               NA               NA 1.435902
      16  0.3534000               NA               NA               NA 1.423901
      17  0.3765220               NA               NA               NA 1.457208
      18  0.3466206               NA               NA               NA 1.414280
      19  0.3669896               NA               NA               NA 1.443383
      20  0.3611331               NA               NA               NA 1.434954
      21  0.3573242               NA               NA               NA 1.429499
      22  0.3659595               NA               NA               NA 1.441897
      23  0.3532680               NA               NA               NA 1.423713
      24  0.3614400               NA               NA               NA 1.435395
      25  0.3548341               NA               NA               NA 1.425944
      26  0.3626380               NA               NA               NA 1.437115
      27  0.3655634               NA               NA               NA 1.441326
      28  0.3527344               NA               NA               NA 1.422953
      29  0.3631120               NA               NA               NA 1.437797
      30  0.3867045               NA               NA               NA 1.472121
      31  0.3519109               NA               NA               NA 1.421782
      32  0.3768405               NA               NA               NA 1.457672
      33  0.3582630               NA               NA               NA 1.430842
      34  0.3587390               NA               NA               NA 1.431523
      35  0.3516387               NA               NA               NA 1.421395
      36  0.3608133               NA               NA               NA 1.434496
      37  0.3544406               NA               NA               NA 1.425383
      38  0.3519254               NA               NA               NA 1.421802
      39  0.3577404               NA               NA               NA 1.430094
      40  0.3699214               NA               NA               NA 1.447621
      41  0.3610235               NA               NA               NA 1.434797
      42  0.3688639               NA               NA               NA 1.446091
      43  0.3683210               NA               NA               NA 1.445306
      44  0.3707242               NA               NA               NA 1.448783
      45  0.3719890               NA               NA               NA 1.450617
      46  0.3471687               NA               NA               NA 1.415055
      47  0.3622725               NA               NA               NA 1.436590
      48  0.3604242               NA               NA               NA 1.433938
      49  0.3470878               NA               NA               NA 1.414941
      50  0.3519288               NA               NA               NA 1.421807
      51  0.3737703               NA               NA               NA 1.453203
      52  0.3730309               NA               NA               NA 1.452129
      53  0.3587298               NA               NA               NA 1.431510
      54  0.3577317               NA               NA               NA 1.430082
      55  0.3670651               NA               NA               NA 1.443492
      56  0.3621821               NA               NA               NA 1.436460
      57  0.3493310               NA               NA               NA 1.418119
      58  0.3611449               NA               NA               NA 1.434971
      59  0.3685236               NA               NA               NA 1.445599
      60  0.3626252               NA               NA               NA 1.437097
      61  0.3565271               NA               NA               NA 1.428360
      62  0.3650248               NA               NA               NA 1.440550
      63  0.3667342               NA               NA               NA 1.443014
      64  0.3536790               NA               NA               NA 1.424298
      65  0.3707512               NA               NA               NA 1.448823
      66  0.3547570               NA               NA               NA 1.425834
      67  0.3556460               NA               NA               NA 1.427102
      68  0.3465922               NA               NA               NA 1.414240
      69  0.3758430               NA               NA               NA 1.456218
      70  0.3856661               NA               NA               NA 1.470594
      71  0.3542125               NA               NA               NA 1.425058
      72  0.3593309               NA               NA               NA 1.432371
      73  0.3657925               NA               NA               NA 1.441656
      74  0.3611311               NA               NA               NA 1.434952
      75  0.3385130               NA               NA               NA 1.402860
      76  0.3738804               NA               NA               NA 1.453363
      77  0.3597065               NA               NA               NA 1.432909
      78  0.3612366               NA               NA               NA 1.435103
      79  0.3607899               NA               NA               NA 1.434462
      80  0.3609283               NA               NA               NA 1.434661
      81  0.3687189               NA               NA               NA 1.445881
      82  0.3664112               NA               NA               NA 1.442548
      83  0.3577425               NA               NA               NA 1.430097
      84  0.3577579               NA               NA               NA 1.430119
      85  0.3578947               NA               NA               NA 1.430315
      86  0.3629637               NA               NA               NA 1.437584
      87  0.3434041               NA               NA               NA 1.409738
      88  0.3523374               NA               NA               NA 1.422388
      89  0.3524220               NA               NA               NA 1.422509
      90  0.3642486               NA               NA               NA 1.439432
      91  0.3577968               NA               NA               NA 1.430175
      92  0.3492491               NA               NA               NA 1.418002
      93  0.3533376               NA               NA               NA 1.423812
      94  0.3530999               NA               NA               NA 1.423473
      95  0.3607553               NA               NA               NA 1.434412
      96  0.3721453               NA               NA               NA 1.450844
      97  0.3600291               NA               NA               NA 1.433371
      98  0.3676785               NA               NA               NA 1.444378
      99  0.3524318               NA               NA               NA 1.422523
      100 0.3438689               NA               NA               NA 1.410394
      
      $m4a$spM_lvlone
                            center       scale
      M1                        NA          NA
      C2               -0.06490582 0.333173465
      M2                        NA          NA
      O2                        NA          NA
      (Intercept)               NA          NA
      M22                       NA          NA
      M23                       NA          NA
      M24                       NA          NA
      O22                       NA          NA
      O23                       NA          NA
      O24                       NA          NA
      abs(C1 - C2)      1.49900534 0.334214181
      log(C1)           0.36049727 0.009050336
      O22:abs(C1 - C2)  0.31342466 0.618807150
      O23:abs(C1 - C2)  0.47068368 0.762352624
      O24:abs(C1 - C2)  0.40568706 0.692690317
      C1                1.43410054 0.012996511
      
      $m4a$mu_reg_norm
      [1] 0
      
      $m4a$tau_reg_norm
      [1] 1e-04
      
      $m4a$shape_tau_norm
      [1] 0.01
      
      $m4a$rate_tau_norm
      [1] 0.01
      
      $m4a$mu_reg_multinomial
      [1] 0
      
      $m4a$tau_reg_multinomial
      [1] 1e-04
      
      $m4a$mu_reg_ordinal
      [1] 0
      
      $m4a$tau_reg_ordinal
      [1] 1e-04
      
      $m4a$mu_delta_ordinal
      [1] 0
      
      $m4a$tau_delta_ordinal
      [1] 1e-04
      
      
      $m4b
      $m4b$M_lvlone
          M1           C2 M2 (Intercept)
      1    1  0.144065882  4           1
      2    2  0.032778478  1           1
      3    2  0.343008492  3           1
      4    1 -0.361887858  3           1
      5    3 -0.389600647  4           1
      6    3 -0.205306841  4           1
      7    3  0.079434830  1           1
      8    3 -0.331246757  1           1
      9    1 -0.329638800  2           1
      10   2  0.167597533  2           1
      11   1  0.860207989  3           1
      12   2  0.022730640  3           1
      13   1  0.217171172  2           1
      14   4 -0.403002412  3           1
      15   2  0.087369742  2           1
      16   3 -0.183870429  1           1
      17   3 -0.194577002  4           1
      18   1 -0.349718516  2           1
      19   2 -0.508781244  3           1
      20   2  0.494883111  3           1
      21   1  0.258041067  2           1
      22   4 -0.922621989  2           1
      23   1  0.431254949  3           1
      24   2 -0.294218881  3           1
      25   1 -0.425548895  2           1
      26   1  0.057176054  2           1
      27   2  0.289090158  1           1
      28   1 -0.473079489  3           1
      29   3 -0.385664863  4           1
      30   1 -0.154780107  2           1
      31   4  0.100536296 NA           1
      32   1  0.634791958  4           1
      33   4 -0.387252617  4           1
      34   2 -0.181741088  4           1
      35   1 -0.311562695  2           1
      36   1 -0.044115907  1           1
      37   1 -0.657409991  3           1
      38   2  0.159577214  4           1
      39   2 -0.460416933  3           1
      40   2           NA  3           1
      41   4 -0.248909867  1           1
      42   4 -0.609021545  4           1
      43   4  0.025471883  1           1
      44   4  0.066648592  2           1
      45   2 -0.276108719  2           1
      46   1 -0.179737577  1           1
      47   3  0.181190937  4           1
      48   3 -0.453871693  2           1
      49   2  0.448629602  4           1
      50   2 -0.529811821  1           1
      51   3 -0.028304571  4           1
      52   1 -0.520318482  4           1
      53   2  0.171317619  4           1
      54   3  0.432732046  3           1
      55   2 -0.346286005  3           1
      56   1 -0.469375653  3           1
      57   4  0.031021711  2           1
      58   1 -0.118837515  3           1
      59   4  0.507769984  3           1
      60   1  0.271797031  4           1
      61   1 -0.124442204  2           1
      62   1  0.277677389  2           1
      63   4 -0.102893730  1           1
      64   1           NA  2           1
      65   2 -0.678303052  2           1
      66   4  0.478880037  3           1
      67   4 -0.428028760  2           1
      68   3  0.048119185  4           1
      69   3  0.216932805 NA           1
      70   2 -0.234575269  1           1
      71   3  0.006827078  2           1
      72   2 -0.456055171  3           1
      73   4  0.346486708  4           1
      74   2  0.205092215  4           1
      75   1 -0.136596858  1           1
      76   3 -0.500179043  4           1
      77   2  0.527352086 NA           1
      78   4  0.022742250  2           1
      79   4           NA  2           1
      80   1 -0.002032440  2           1
      81   1 -0.154246160  4           1
      82   4  0.140201825  3           1
      83   3 -0.141417121  3           1
      84   4           NA  1           1
      85   2 -0.021285339  2           1
      86   4 -0.010196306  1           1
      87   3 -0.089747520  3           1
      88   3 -0.083699898  1           1
      89   3 -0.044061996  2           1
      90   1 -0.209291697  1           1
      91   1  0.639036426  3           1
      92   1  0.094698299  1           1
      93   1 -0.055510622  4           1
      94   3 -0.421318463  4           1
      95   2  0.125295503  1           1
      96   1  0.213084904  4           1
      97   3 -0.161914659  4           1
      98   4 -0.034767685  3           1
      99   2 -0.320681689  3           1
      100  1  0.058192962  4           1
          ifelse(as.numeric(M2) > as.numeric(O1), 1, 0) abs(C1 - C2)   log(C1)
      1                                              NA           NA 0.3439662
      2                                              NA           NA 0.3605954
      3                                              NA           NA 0.3583696
      4                                              NA           NA 0.3736964
      5                                              NA           NA 0.3634928
      6                                              NA           NA 0.3737730
      7                                              NA           NA 0.3542952
      8                                              NA           NA 0.3631892
      9                                              NA           NA 0.3484794
      10                                             NA           NA 0.3706241
      11                                             NA           NA 0.3565373
      12                                             NA           NA 0.3716534
      13                                             NA           NA 0.3510408
      14                                             NA           NA 0.3527707
      15                                             NA           NA 0.3617934
      16                                             NA           NA 0.3534000
      17                                             NA           NA 0.3765220
      18                                             NA           NA 0.3466206
      19                                             NA           NA 0.3669896
      20                                             NA           NA 0.3611331
      21                                             NA           NA 0.3573242
      22                                             NA           NA 0.3659595
      23                                             NA           NA 0.3532680
      24                                             NA           NA 0.3614400
      25                                             NA           NA 0.3548341
      26                                             NA           NA 0.3626380
      27                                             NA           NA 0.3655634
      28                                             NA           NA 0.3527344
      29                                             NA           NA 0.3631120
      30                                             NA           NA 0.3867045
      31                                             NA           NA 0.3519109
      32                                             NA           NA 0.3768405
      33                                             NA           NA 0.3582630
      34                                             NA           NA 0.3587390
      35                                             NA           NA 0.3516387
      36                                             NA           NA 0.3608133
      37                                             NA           NA 0.3544406
      38                                             NA           NA 0.3519254
      39                                             NA           NA 0.3577404
      40                                             NA           NA 0.3699214
      41                                             NA           NA 0.3610235
      42                                             NA           NA 0.3688639
      43                                             NA           NA 0.3683210
      44                                             NA           NA 0.3707242
      45                                             NA           NA 0.3719890
      46                                             NA           NA 0.3471687
      47                                             NA           NA 0.3622725
      48                                             NA           NA 0.3604242
      49                                             NA           NA 0.3470878
      50                                             NA           NA 0.3519288
      51                                             NA           NA 0.3737703
      52                                             NA           NA 0.3730309
      53                                             NA           NA 0.3587298
      54                                             NA           NA 0.3577317
      55                                             NA           NA 0.3670651
      56                                             NA           NA 0.3621821
      57                                             NA           NA 0.3493310
      58                                             NA           NA 0.3611449
      59                                             NA           NA 0.3685236
      60                                             NA           NA 0.3626252
      61                                             NA           NA 0.3565271
      62                                             NA           NA 0.3650248
      63                                             NA           NA 0.3667342
      64                                             NA           NA 0.3536790
      65                                             NA           NA 0.3707512
      66                                             NA           NA 0.3547570
      67                                             NA           NA 0.3556460
      68                                             NA           NA 0.3465922
      69                                             NA           NA 0.3758430
      70                                             NA           NA 0.3856661
      71                                             NA           NA 0.3542125
      72                                             NA           NA 0.3593309
      73                                             NA           NA 0.3657925
      74                                             NA           NA 0.3611311
      75                                             NA           NA 0.3385130
      76                                             NA           NA 0.3738804
      77                                             NA           NA 0.3597065
      78                                             NA           NA 0.3612366
      79                                             NA           NA 0.3607899
      80                                             NA           NA 0.3609283
      81                                             NA           NA 0.3687189
      82                                             NA           NA 0.3664112
      83                                             NA           NA 0.3577425
      84                                             NA           NA 0.3577579
      85                                             NA           NA 0.3578947
      86                                             NA           NA 0.3629637
      87                                             NA           NA 0.3434041
      88                                             NA           NA 0.3523374
      89                                             NA           NA 0.3524220
      90                                             NA           NA 0.3642486
      91                                             NA           NA 0.3577968
      92                                             NA           NA 0.3492491
      93                                             NA           NA 0.3533376
      94                                             NA           NA 0.3530999
      95                                             NA           NA 0.3607553
      96                                             NA           NA 0.3721453
      97                                             NA           NA 0.3600291
      98                                             NA           NA 0.3676785
      99                                             NA           NA 0.3524318
      100                                            NA           NA 0.3438689
          ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2) M22 M23 M24
      1                                                           NA  NA  NA  NA
      2                                                           NA  NA  NA  NA
      3                                                           NA  NA  NA  NA
      4                                                           NA  NA  NA  NA
      5                                                           NA  NA  NA  NA
      6                                                           NA  NA  NA  NA
      7                                                           NA  NA  NA  NA
      8                                                           NA  NA  NA  NA
      9                                                           NA  NA  NA  NA
      10                                                          NA  NA  NA  NA
      11                                                          NA  NA  NA  NA
      12                                                          NA  NA  NA  NA
      13                                                          NA  NA  NA  NA
      14                                                          NA  NA  NA  NA
      15                                                          NA  NA  NA  NA
      16                                                          NA  NA  NA  NA
      17                                                          NA  NA  NA  NA
      18                                                          NA  NA  NA  NA
      19                                                          NA  NA  NA  NA
      20                                                          NA  NA  NA  NA
      21                                                          NA  NA  NA  NA
      22                                                          NA  NA  NA  NA
      23                                                          NA  NA  NA  NA
      24                                                          NA  NA  NA  NA
      25                                                          NA  NA  NA  NA
      26                                                          NA  NA  NA  NA
      27                                                          NA  NA  NA  NA
      28                                                          NA  NA  NA  NA
      29                                                          NA  NA  NA  NA
      30                                                          NA  NA  NA  NA
      31                                                          NA  NA  NA  NA
      32                                                          NA  NA  NA  NA
      33                                                          NA  NA  NA  NA
      34                                                          NA  NA  NA  NA
      35                                                          NA  NA  NA  NA
      36                                                          NA  NA  NA  NA
      37                                                          NA  NA  NA  NA
      38                                                          NA  NA  NA  NA
      39                                                          NA  NA  NA  NA
      40                                                          NA  NA  NA  NA
      41                                                          NA  NA  NA  NA
      42                                                          NA  NA  NA  NA
      43                                                          NA  NA  NA  NA
      44                                                          NA  NA  NA  NA
      45                                                          NA  NA  NA  NA
      46                                                          NA  NA  NA  NA
      47                                                          NA  NA  NA  NA
      48                                                          NA  NA  NA  NA
      49                                                          NA  NA  NA  NA
      50                                                          NA  NA  NA  NA
      51                                                          NA  NA  NA  NA
      52                                                          NA  NA  NA  NA
      53                                                          NA  NA  NA  NA
      54                                                          NA  NA  NA  NA
      55                                                          NA  NA  NA  NA
      56                                                          NA  NA  NA  NA
      57                                                          NA  NA  NA  NA
      58                                                          NA  NA  NA  NA
      59                                                          NA  NA  NA  NA
      60                                                          NA  NA  NA  NA
      61                                                          NA  NA  NA  NA
      62                                                          NA  NA  NA  NA
      63                                                          NA  NA  NA  NA
      64                                                          NA  NA  NA  NA
      65                                                          NA  NA  NA  NA
      66                                                          NA  NA  NA  NA
      67                                                          NA  NA  NA  NA
      68                                                          NA  NA  NA  NA
      69                                                          NA  NA  NA  NA
      70                                                          NA  NA  NA  NA
      71                                                          NA  NA  NA  NA
      72                                                          NA  NA  NA  NA
      73                                                          NA  NA  NA  NA
      74                                                          NA  NA  NA  NA
      75                                                          NA  NA  NA  NA
      76                                                          NA  NA  NA  NA
      77                                                          NA  NA  NA  NA
      78                                                          NA  NA  NA  NA
      79                                                          NA  NA  NA  NA
      80                                                          NA  NA  NA  NA
      81                                                          NA  NA  NA  NA
      82                                                          NA  NA  NA  NA
      83                                                          NA  NA  NA  NA
      84                                                          NA  NA  NA  NA
      85                                                          NA  NA  NA  NA
      86                                                          NA  NA  NA  NA
      87                                                          NA  NA  NA  NA
      88                                                          NA  NA  NA  NA
      89                                                          NA  NA  NA  NA
      90                                                          NA  NA  NA  NA
      91                                                          NA  NA  NA  NA
      92                                                          NA  NA  NA  NA
      93                                                          NA  NA  NA  NA
      94                                                          NA  NA  NA  NA
      95                                                          NA  NA  NA  NA
      96                                                          NA  NA  NA  NA
      97                                                          NA  NA  NA  NA
      98                                                          NA  NA  NA  NA
      99                                                          NA  NA  NA  NA
      100                                                         NA  NA  NA  NA
                O1.L O1.Q       O1.C       C1 O1
      1   -0.2236068 -0.5  0.6708204 1.410531  2
      2    0.6708204  0.5  0.2236068 1.434183  4
      3    0.2236068 -0.5 -0.6708204 1.430994  3
      4   -0.2236068 -0.5  0.6708204 1.453096  2
      5    0.2236068 -0.5 -0.6708204 1.438344  3
      6   -0.6708204  0.5 -0.2236068 1.453207  1
      7    0.2236068 -0.5 -0.6708204 1.425176  3
      8    0.6708204  0.5  0.2236068 1.437908  4
      9    0.6708204  0.5  0.2236068 1.416911  4
      10  -0.2236068 -0.5  0.6708204 1.448638  2
      11  -0.6708204  0.5 -0.2236068 1.428375  1
      12   0.2236068 -0.5 -0.6708204 1.450130  3
      13   0.2236068 -0.5 -0.6708204 1.420545  3
      14  -0.6708204  0.5 -0.2236068 1.423005  1
      15  -0.6708204  0.5 -0.2236068 1.435902  1
      16   0.6708204  0.5  0.2236068 1.423901  4
      17  -0.2236068 -0.5  0.6708204 1.457208  2
      18   0.2236068 -0.5 -0.6708204 1.414280  3
      19   0.6708204  0.5  0.2236068 1.443383  4
      20  -0.6708204  0.5 -0.2236068 1.434954  1
      21   0.2236068 -0.5 -0.6708204 1.429499  3
      22   0.6708204  0.5  0.2236068 1.441897  4
      23   0.6708204  0.5  0.2236068 1.423713  4
      24  -0.2236068 -0.5  0.6708204 1.435395  2
      25  -0.6708204  0.5 -0.2236068 1.425944  1
      26   0.2236068 -0.5 -0.6708204 1.437115  3
      27   0.6708204  0.5  0.2236068 1.441326  4
      28  -0.6708204  0.5 -0.2236068 1.422953  1
      29   0.6708204  0.5  0.2236068 1.437797  4
      30   0.6708204  0.5  0.2236068 1.472121  4
      31  -0.2236068 -0.5  0.6708204 1.421782  2
      32   0.2236068 -0.5 -0.6708204 1.457672  3
      33   0.2236068 -0.5 -0.6708204 1.430842  3
      34  -0.6708204  0.5 -0.2236068 1.431523  1
      35  -0.6708204  0.5 -0.2236068 1.421395  1
      36   0.6708204  0.5  0.2236068 1.434496  4
      37   0.6708204  0.5  0.2236068 1.425383  4
      38   0.6708204  0.5  0.2236068 1.421802  4
      39  -0.6708204  0.5 -0.2236068 1.430094  1
      40  -0.2236068 -0.5  0.6708204 1.447621  2
      41  -0.6708204  0.5 -0.2236068 1.434797  1
      42  -0.6708204  0.5 -0.2236068 1.446091  1
      43  -0.2236068 -0.5  0.6708204 1.445306  2
      44  -0.2236068 -0.5  0.6708204 1.448783  2
      45  -0.6708204  0.5 -0.2236068 1.450617  1
      46  -0.6708204  0.5 -0.2236068 1.415055  1
      47   0.6708204  0.5  0.2236068 1.436590  4
      48   0.6708204  0.5  0.2236068 1.433938  4
      49  -0.2236068 -0.5  0.6708204 1.414941  2
      50  -0.2236068 -0.5  0.6708204 1.421807  2
      51  -0.6708204  0.5 -0.2236068 1.453203  1
      52   0.2236068 -0.5 -0.6708204 1.452129  3
      53  -0.6708204  0.5 -0.2236068 1.431510  1
      54   0.2236068 -0.5 -0.6708204 1.430082  3
      55  -0.2236068 -0.5  0.6708204 1.443492  2
      56   0.6708204  0.5  0.2236068 1.436460  4
      57  -0.2236068 -0.5  0.6708204 1.418119  2
      58  -0.6708204  0.5 -0.2236068 1.434971  1
      59  -0.6708204  0.5 -0.2236068 1.445599  1
      60   0.6708204  0.5  0.2236068 1.437097  4
      61  -0.2236068 -0.5  0.6708204 1.428360  2
      62   0.6708204  0.5  0.2236068 1.440550  4
      63   0.2236068 -0.5 -0.6708204 1.443014  3
      64  -0.2236068 -0.5  0.6708204 1.424298  2
      65   0.2236068 -0.5 -0.6708204 1.448823  3
      66   0.2236068 -0.5 -0.6708204 1.425834  3
      67  -0.2236068 -0.5  0.6708204 1.427102  2
      68  -0.6708204  0.5 -0.2236068 1.414240  1
      69  -0.6708204  0.5 -0.2236068 1.456218  1
      70  -0.6708204  0.5 -0.2236068 1.470594  1
      71  -0.6708204  0.5 -0.2236068 1.425058  1
      72   0.2236068 -0.5 -0.6708204 1.432371  3
      73  -0.2236068 -0.5  0.6708204 1.441656  2
      74  -0.2236068 -0.5  0.6708204 1.434952  2
      75   0.2236068 -0.5 -0.6708204 1.402860  3
      76   0.2236068 -0.5 -0.6708204 1.453363  3
      77   0.6708204  0.5  0.2236068 1.432909  4
      78   0.2236068 -0.5 -0.6708204 1.435103  3
      79  -0.2236068 -0.5  0.6708204 1.434462  2
      80  -0.2236068 -0.5  0.6708204 1.434661  2
      81   0.2236068 -0.5 -0.6708204 1.445881  3
      82  -0.6708204  0.5 -0.2236068 1.442548  1
      83   0.2236068 -0.5 -0.6708204 1.430097  3
      84  -0.2236068 -0.5  0.6708204 1.430119  2
      85  -0.2236068 -0.5  0.6708204 1.430315  2
      86   0.6708204  0.5  0.2236068 1.437584  4
      87   0.2236068 -0.5 -0.6708204 1.409738  3
      88  -0.2236068 -0.5  0.6708204 1.422388  2
      89   0.2236068 -0.5 -0.6708204 1.422509  3
      90   0.2236068 -0.5 -0.6708204 1.439432  3
      91   0.6708204  0.5  0.2236068 1.430175  4
      92  -0.6708204  0.5 -0.2236068 1.418002  1
      93   0.6708204  0.5  0.2236068 1.423812  4
      94  -0.6708204  0.5 -0.2236068 1.423473  1
      95  -0.6708204  0.5 -0.2236068 1.434412  1
      96   0.2236068 -0.5 -0.6708204 1.450844  3
      97  -0.6708204  0.5 -0.2236068 1.433371  1
      98   0.2236068 -0.5 -0.6708204 1.444378  3
      99   0.2236068 -0.5 -0.6708204 1.422523  3
      100  0.2236068 -0.5 -0.6708204 1.410394  3
      
      $m4b$spM_lvlone
                                                                      center
      M1                                                                  NA
      C2                                                         -0.06490582
      M2                                                                  NA
      (Intercept)                                                         NA
      ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)               0.39175258
      abs(C1 - C2)                                                1.49900534
      log(C1)                                                     0.36049727
      ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)  0.60211251
      M22                                                                 NA
      M23                                                                 NA
      M24                                                                 NA
      O1.L                                                                NA
      O1.Q                                                                NA
      O1.C                                                                NA
      C1                                                          1.43410054
      O1                                                                  NA
                                                                       scale
      M1                                                                  NA
      C2                                                         0.333173465
      M2                                                                  NA
      (Intercept)                                                         NA
      ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)              0.490677700
      abs(C1 - C2)                                               0.334214181
      log(C1)                                                    0.009050336
      ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2) 0.778929778
      M22                                                                 NA
      M23                                                                 NA
      M24                                                                 NA
      O1.L                                                                NA
      O1.Q                                                                NA
      O1.C                                                                NA
      C1                                                         0.012996511
      O1                                                                  NA
      
      $m4b$mu_reg_norm
      [1] 0
      
      $m4b$tau_reg_norm
      [1] 1e-04
      
      $m4b$shape_tau_norm
      [1] 0.01
      
      $m4b$rate_tau_norm
      [1] 0.01
      
      $m4b$mu_reg_multinomial
      [1] 0
      
      $m4b$tau_reg_multinomial
      [1] 1e-04
      
      

# jagsmodel remains the same

    Code
      lapply(models, "[[", "jagsmodel")
    Output
      $m0a
      model { 
      
         # Multinomial logit model for M1 ------------------------------------------------
        for (i in 1:100) {
          M_lvlone[i, 1] ~ dcat(p_M1[i, 1:4])
      
          p_M1[i, 1] <- min(1-1e-7, max(1e-7, phi_M1[i, 1] / sum(phi_M1[i, ])))
          p_M1[i, 2] <- min(1-1e-7, max(1e-7, phi_M1[i, 2] / sum(phi_M1[i, ])))
          p_M1[i, 3] <- min(1-1e-7, max(1e-7, phi_M1[i, 3] / sum(phi_M1[i, ])))
          p_M1[i, 4] <- min(1-1e-7, max(1e-7, phi_M1[i, 4] / sum(phi_M1[i, ])))
      
          log(phi_M1[i, 1]) <- 0
          log(phi_M1[i, 2]) <- M_lvlone[i, 2] * beta[1]
          log(phi_M1[i, 3]) <- M_lvlone[i, 2] * beta[2]
          log(phi_M1[i, 4]) <- M_lvlone[i, 2] * beta[3]
        }
      
        # Priors for the model for M1
        for (k in 1:3) {
          beta[k] ~ dnorm(mu_reg_multinomial, tau_reg_multinomial)
        }
       
       }
      $m0b
      model { 
      
         # Multinomial logit model for M2 ------------------------------------------------
        for (i in 1:100) {
          M_lvlone[i, 1] ~ dcat(p_M2[i, 1:4])
      
          p_M2[i, 1] <- min(1-1e-7, max(1e-7, phi_M2[i, 1] / sum(phi_M2[i, ])))
          p_M2[i, 2] <- min(1-1e-7, max(1e-7, phi_M2[i, 2] / sum(phi_M2[i, ])))
          p_M2[i, 3] <- min(1-1e-7, max(1e-7, phi_M2[i, 3] / sum(phi_M2[i, ])))
          p_M2[i, 4] <- min(1-1e-7, max(1e-7, phi_M2[i, 4] / sum(phi_M2[i, ])))
      
          log(phi_M2[i, 1]) <- 0
          log(phi_M2[i, 2]) <- M_lvlone[i, 2] * beta[1]
          log(phi_M2[i, 3]) <- M_lvlone[i, 2] * beta[2]
          log(phi_M2[i, 4]) <- M_lvlone[i, 2] * beta[3]
        }
      
        # Priors for the model for M2
        for (k in 1:3) {
          beta[k] ~ dnorm(mu_reg_multinomial, tau_reg_multinomial)
        }
       
       }
      $m1a
      model { 
      
         # Multinomial logit model for M1 ------------------------------------------------
        for (i in 1:100) {
          M_lvlone[i, 1] ~ dcat(p_M1[i, 1:4])
      
          p_M1[i, 1] <- min(1-1e-7, max(1e-7, phi_M1[i, 1] / sum(phi_M1[i, ])))
          p_M1[i, 2] <- min(1-1e-7, max(1e-7, phi_M1[i, 2] / sum(phi_M1[i, ])))
          p_M1[i, 3] <- min(1-1e-7, max(1e-7, phi_M1[i, 3] / sum(phi_M1[i, ])))
          p_M1[i, 4] <- min(1-1e-7, max(1e-7, phi_M1[i, 4] / sum(phi_M1[i, ])))
      
          log(phi_M1[i, 1]) <- 0
          log(phi_M1[i, 2]) <- M_lvlone[i, 2] * beta[1] +
                               (M_lvlone[i, 3] - spM_lvlone[3, 1])/spM_lvlone[3, 2] * beta[2]
          log(phi_M1[i, 3]) <- M_lvlone[i, 2] * beta[3] +
                               (M_lvlone[i, 3] - spM_lvlone[3, 1])/spM_lvlone[3, 2] * beta[4]
          log(phi_M1[i, 4]) <- M_lvlone[i, 2] * beta[5] +
                               (M_lvlone[i, 3] - spM_lvlone[3, 1])/spM_lvlone[3, 2] * beta[6]
        }
      
        # Priors for the model for M1
        for (k in 1:6) {
          beta[k] ~ dnorm(mu_reg_multinomial, tau_reg_multinomial)
        }
       
       }
      $m1b
      model { 
      
         # Multinomial logit model for M2 ------------------------------------------------
        for (i in 1:100) {
          M_lvlone[i, 1] ~ dcat(p_M2[i, 1:4])
      
          p_M2[i, 1] <- min(1-1e-7, max(1e-7, phi_M2[i, 1] / sum(phi_M2[i, ])))
          p_M2[i, 2] <- min(1-1e-7, max(1e-7, phi_M2[i, 2] / sum(phi_M2[i, ])))
          p_M2[i, 3] <- min(1-1e-7, max(1e-7, phi_M2[i, 3] / sum(phi_M2[i, ])))
          p_M2[i, 4] <- min(1-1e-7, max(1e-7, phi_M2[i, 4] / sum(phi_M2[i, ])))
      
          log(phi_M2[i, 1]) <- 0
          log(phi_M2[i, 2]) <- M_lvlone[i, 2] * beta[1] +
                               (M_lvlone[i, 3] - spM_lvlone[3, 1])/spM_lvlone[3, 2] * beta[2]
          log(phi_M2[i, 3]) <- M_lvlone[i, 2] * beta[3] +
                               (M_lvlone[i, 3] - spM_lvlone[3, 1])/spM_lvlone[3, 2] * beta[4]
          log(phi_M2[i, 4]) <- M_lvlone[i, 2] * beta[5] +
                               (M_lvlone[i, 3] - spM_lvlone[3, 1])/spM_lvlone[3, 2] * beta[6]
        }
      
        # Priors for the model for M2
        for (k in 1:6) {
          beta[k] ~ dnorm(mu_reg_multinomial, tau_reg_multinomial)
        }
       
       }
      $m2a
      model { 
      
         # Multinomial logit model for M1 ------------------------------------------------
        for (i in 1:100) {
          M_lvlone[i, 1] ~ dcat(p_M1[i, 1:4])
      
          p_M1[i, 1] <- min(1-1e-7, max(1e-7, phi_M1[i, 1] / sum(phi_M1[i, ])))
          p_M1[i, 2] <- min(1-1e-7, max(1e-7, phi_M1[i, 2] / sum(phi_M1[i, ])))
          p_M1[i, 3] <- min(1-1e-7, max(1e-7, phi_M1[i, 3] / sum(phi_M1[i, ])))
          p_M1[i, 4] <- min(1-1e-7, max(1e-7, phi_M1[i, 4] / sum(phi_M1[i, ])))
      
          log(phi_M1[i, 1]) <- 0
          log(phi_M1[i, 2]) <- M_lvlone[i, 3] * beta[1] +
                               (M_lvlone[i, 2] - spM_lvlone[2, 1])/spM_lvlone[2, 2] * beta[2]
          log(phi_M1[i, 3]) <- M_lvlone[i, 3] * beta[3] +
                               (M_lvlone[i, 2] - spM_lvlone[2, 1])/spM_lvlone[2, 2] * beta[4]
          log(phi_M1[i, 4]) <- M_lvlone[i, 3] * beta[5] +
                               (M_lvlone[i, 2] - spM_lvlone[2, 1])/spM_lvlone[2, 2] * beta[6]
        }
      
        # Priors for the model for M1
        for (k in 1:6) {
          beta[k] ~ dnorm(mu_reg_multinomial, tau_reg_multinomial)
        }
      
      
      
        # Normal model for C2 -----------------------------------------------------------
        for (i in 1:100) {
          M_lvlone[i, 2] ~ dnorm(mu_C2[i], tau_C2)
          mu_C2[i] <- M_lvlone[i, 3] * alpha[1]
        }
      
        # Priors for the model for C2
        for (k in 1:1) {
          alpha[k] ~ dnorm(mu_reg_norm, tau_reg_norm)
        }
        tau_C2 ~ dgamma(shape_tau_norm, rate_tau_norm)
        sigma_C2 <- sqrt(1/tau_C2)
       
       }
      $m2b
      model { 
      
         # Multinomial logit model for M2 ------------------------------------------------
        for (i in 1:100) {
          M_lvlone[i, 1] ~ dcat(p_M2[i, 1:4])
      
          p_M2[i, 1] <- min(1-1e-7, max(1e-7, phi_M2[i, 1] / sum(phi_M2[i, ])))
          p_M2[i, 2] <- min(1-1e-7, max(1e-7, phi_M2[i, 2] / sum(phi_M2[i, ])))
          p_M2[i, 3] <- min(1-1e-7, max(1e-7, phi_M2[i, 3] / sum(phi_M2[i, ])))
          p_M2[i, 4] <- min(1-1e-7, max(1e-7, phi_M2[i, 4] / sum(phi_M2[i, ])))
      
          log(phi_M2[i, 1]) <- 0
          log(phi_M2[i, 2]) <- M_lvlone[i, 3] * beta[1] +
                               (M_lvlone[i, 2] - spM_lvlone[2, 1])/spM_lvlone[2, 2] * beta[2]
          log(phi_M2[i, 3]) <- M_lvlone[i, 3] * beta[3] +
                               (M_lvlone[i, 2] - spM_lvlone[2, 1])/spM_lvlone[2, 2] * beta[4]
          log(phi_M2[i, 4]) <- M_lvlone[i, 3] * beta[5] +
                               (M_lvlone[i, 2] - spM_lvlone[2, 1])/spM_lvlone[2, 2] * beta[6]
        }
      
        # Priors for the model for M2
        for (k in 1:6) {
          beta[k] ~ dnorm(mu_reg_multinomial, tau_reg_multinomial)
        }
      
      
      
        # Normal model for C2 -----------------------------------------------------------
        for (i in 1:100) {
          M_lvlone[i, 2] ~ dnorm(mu_C2[i], tau_C2)
          mu_C2[i] <- M_lvlone[i, 3] * alpha[1]
        }
      
        # Priors for the model for C2
        for (k in 1:1) {
          alpha[k] ~ dnorm(mu_reg_norm, tau_reg_norm)
        }
        tau_C2 ~ dgamma(shape_tau_norm, rate_tau_norm)
        sigma_C2 <- sqrt(1/tau_C2)
       
       }
      $m3a
      model { 
      
         # Normal model for C1 -----------------------------------------------------------
        for (i in 1:100) {
          M_lvlone[i, 1] ~ dnorm(mu_C1[i], tau_C1)
          mu_C1[i] <- M_lvlone[i, 2] * beta[1] + M_lvlone[i, 3] * beta[2] +
                      M_lvlone[i, 4] * beta[3] + M_lvlone[i, 5] * beta[4]
        }
      
        # Priors for the model for C1
        for (k in 1:4) {
          beta[k] ~ dnorm(mu_reg_norm, tau_reg_norm)
        }
        tau_C1 ~ dgamma(shape_tau_norm, rate_tau_norm)
        sigma_C1 <- sqrt(1/tau_C1)
       
       }
      $m3b
      model { 
      
         # Normal model for C1 -----------------------------------------------------------
        for (i in 1:100) {
          M_lvlone[i, 1] ~ dnorm(mu_C1[i], tau_C1)
          mu_C1[i] <- M_lvlone[i, 3] * beta[1] + M_lvlone[i, 4] * beta[2] +
                      M_lvlone[i, 5] * beta[3] + M_lvlone[i, 6] * beta[4]
        }
      
        # Priors for the model for C1
        for (k in 1:4) {
          beta[k] ~ dnorm(mu_reg_norm, tau_reg_norm)
        }
        tau_C1 ~ dgamma(shape_tau_norm, rate_tau_norm)
        sigma_C1 <- sqrt(1/tau_C1)
      
      
      
        # Multinomial logit model for M2 ------------------------------------------------
        for (i in 1:100) {
          M_lvlone[i, 2] ~ dcat(p_M2[i, 1:4])
      
          p_M2[i, 1] <- min(1-1e-7, max(1e-7, phi_M2[i, 1] / sum(phi_M2[i, ])))
          p_M2[i, 2] <- min(1-1e-7, max(1e-7, phi_M2[i, 2] / sum(phi_M2[i, ])))
          p_M2[i, 3] <- min(1-1e-7, max(1e-7, phi_M2[i, 3] / sum(phi_M2[i, ])))
          p_M2[i, 4] <- min(1-1e-7, max(1e-7, phi_M2[i, 4] / sum(phi_M2[i, ])))
      
          log(phi_M2[i, 1]) <- 0
          log(phi_M2[i, 2]) <- M_lvlone[i, 3] * alpha[1]
          log(phi_M2[i, 3]) <- M_lvlone[i, 3] * alpha[2]
          log(phi_M2[i, 4]) <- M_lvlone[i, 3] * alpha[3]
      
          M_lvlone[i, 4] <- ifelse(M_lvlone[i, 2] == 2, 1, 0)
          M_lvlone[i, 5] <- ifelse(M_lvlone[i, 2] == 3, 1, 0)
          M_lvlone[i, 6] <- ifelse(M_lvlone[i, 2] == 4, 1, 0)
      
        }
      
        # Priors for the model for M2
        for (k in 1:3) {
          alpha[k] ~ dnorm(mu_reg_multinomial, tau_reg_multinomial)
        }
       
       }
      $m4a
      model { 
      
         # Multinomial logit model for M1 ------------------------------------------------
        for (i in 1:100) {
          M_lvlone[i, 1] ~ dcat(p_M1[i, 1:4])
      
          p_M1[i, 1] <- min(1-1e-7, max(1e-7, phi_M1[i, 1] / sum(phi_M1[i, ])))
          p_M1[i, 2] <- min(1-1e-7, max(1e-7, phi_M1[i, 2] / sum(phi_M1[i, ])))
          p_M1[i, 3] <- min(1-1e-7, max(1e-7, phi_M1[i, 3] / sum(phi_M1[i, ])))
          p_M1[i, 4] <- min(1-1e-7, max(1e-7, phi_M1[i, 4] / sum(phi_M1[i, ])))
      
          log(phi_M1[i, 1]) <- 0
          log(phi_M1[i, 2]) <- M_lvlone[i, 5] * beta[1] + M_lvlone[i, 6] * beta[2] +
                               M_lvlone[i, 7] * beta[3] + M_lvlone[i, 8] * beta[4] +
                               M_lvlone[i, 9] * beta[5] + M_lvlone[i, 10] * beta[6] +
                               M_lvlone[i, 11] * beta[7] +
                               (M_lvlone[i, 12] - spM_lvlone[12, 1])/spM_lvlone[12, 2] * beta[8] +
                               (M_lvlone[i, 13] - spM_lvlone[13, 1])/spM_lvlone[13, 2] * beta[9] +
                               (M_lvlone[i, 14] - spM_lvlone[14, 1])/spM_lvlone[14, 2] * beta[10] +
                               (M_lvlone[i, 15] - spM_lvlone[15, 1])/spM_lvlone[15, 2] * beta[11] +
                               (M_lvlone[i, 16] - spM_lvlone[16, 1])/spM_lvlone[16, 2] * beta[12]
          log(phi_M1[i, 3]) <- M_lvlone[i, 5] * beta[13] + M_lvlone[i, 6] * beta[14] +
                               M_lvlone[i, 7] * beta[15] + M_lvlone[i, 8] * beta[16] +
                               M_lvlone[i, 9] * beta[17] + M_lvlone[i, 10] * beta[18] +
                               M_lvlone[i, 11] * beta[19] +
                               (M_lvlone[i, 12] - spM_lvlone[12, 1])/spM_lvlone[12, 2] * beta[20] +
                               (M_lvlone[i, 13] - spM_lvlone[13, 1])/spM_lvlone[13, 2] * beta[21] +
                               (M_lvlone[i, 14] - spM_lvlone[14, 1])/spM_lvlone[14, 2] * beta[22] +
                               (M_lvlone[i, 15] - spM_lvlone[15, 1])/spM_lvlone[15, 2] * beta[23] +
                               (M_lvlone[i, 16] - spM_lvlone[16, 1])/spM_lvlone[16, 2] * beta[24]
          log(phi_M1[i, 4]) <- M_lvlone[i, 5] * beta[25] + M_lvlone[i, 6] * beta[26] +
                               M_lvlone[i, 7] * beta[27] + M_lvlone[i, 8] * beta[28] +
                               M_lvlone[i, 9] * beta[29] + M_lvlone[i, 10] * beta[30] +
                               M_lvlone[i, 11] * beta[31] +
                               (M_lvlone[i, 12] - spM_lvlone[12, 1])/spM_lvlone[12, 2] * beta[32] +
                               (M_lvlone[i, 13] - spM_lvlone[13, 1])/spM_lvlone[13, 2] * beta[33] +
                               (M_lvlone[i, 14] - spM_lvlone[14, 1])/spM_lvlone[14, 2] * beta[34] +
                               (M_lvlone[i, 15] - spM_lvlone[15, 1])/spM_lvlone[15, 2] * beta[35] +
                               (M_lvlone[i, 16] - spM_lvlone[16, 1])/spM_lvlone[16, 2] * beta[36]
        }
      
        # Priors for the model for M1
        for (k in 1:36) {
          beta[k] ~ dnorm(mu_reg_multinomial, tau_reg_multinomial)
        }
      
      
      
        # Normal model for C2 -----------------------------------------------------------
        for (i in 1:100) {
          M_lvlone[i, 2] ~ dnorm(mu_C2[i], tau_C2)
          mu_C2[i] <- M_lvlone[i, 5] * alpha[1] + M_lvlone[i, 6] * alpha[2] +
                      M_lvlone[i, 7] * alpha[3] + M_lvlone[i, 8] * alpha[4] +
                      M_lvlone[i, 9] * alpha[5] + M_lvlone[i, 10] * alpha[6] +
                      M_lvlone[i, 11] * alpha[7] +
                      (M_lvlone[i, 17] - spM_lvlone[17, 1])/spM_lvlone[17, 2] * alpha[8]
      
          M_lvlone[i, 12] <- abs(M_lvlone[i, 17] - M_lvlone[i, 2])
      
      
        }
      
        # Priors for the model for C2
        for (k in 1:8) {
          alpha[k] ~ dnorm(mu_reg_norm, tau_reg_norm)
        }
        tau_C2 ~ dgamma(shape_tau_norm, rate_tau_norm)
        sigma_C2 <- sqrt(1/tau_C2)
      
      
      
        # Multinomial logit model for M2 ------------------------------------------------
        for (i in 1:100) {
          M_lvlone[i, 3] ~ dcat(p_M2[i, 1:4])
      
          p_M2[i, 1] <- min(1-1e-7, max(1e-7, phi_M2[i, 1] / sum(phi_M2[i, ])))
          p_M2[i, 2] <- min(1-1e-7, max(1e-7, phi_M2[i, 2] / sum(phi_M2[i, ])))
          p_M2[i, 3] <- min(1-1e-7, max(1e-7, phi_M2[i, 3] / sum(phi_M2[i, ])))
          p_M2[i, 4] <- min(1-1e-7, max(1e-7, phi_M2[i, 4] / sum(phi_M2[i, ])))
      
          log(phi_M2[i, 1]) <- 0
          log(phi_M2[i, 2]) <- M_lvlone[i, 5] * alpha[9] + M_lvlone[i, 9] * alpha[10] +
                               M_lvlone[i, 10] * alpha[11] + M_lvlone[i, 11] * alpha[12] +
                               (M_lvlone[i, 17] - spM_lvlone[17, 1])/spM_lvlone[17, 2] * alpha[13]
          log(phi_M2[i, 3]) <- M_lvlone[i, 5] * alpha[14] + M_lvlone[i, 9] * alpha[15] +
                               M_lvlone[i, 10] * alpha[16] + M_lvlone[i, 11] * alpha[17] +
                               (M_lvlone[i, 17] - spM_lvlone[17, 1])/spM_lvlone[17, 2] * alpha[18]
          log(phi_M2[i, 4]) <- M_lvlone[i, 5] * alpha[19] + M_lvlone[i, 9] * alpha[20] +
                               M_lvlone[i, 10] * alpha[21] + M_lvlone[i, 11] * alpha[22] +
                               (M_lvlone[i, 17] - spM_lvlone[17, 1])/spM_lvlone[17, 2] * alpha[23]
      
          M_lvlone[i, 6] <- ifelse(M_lvlone[i, 3] == 2, 1, 0)
          M_lvlone[i, 7] <- ifelse(M_lvlone[i, 3] == 3, 1, 0)
          M_lvlone[i, 8] <- ifelse(M_lvlone[i, 3] == 4, 1, 0)
      
        }
      
        # Priors for the model for M2
        for (k in 9:23) {
          alpha[k] ~ dnorm(mu_reg_multinomial, tau_reg_multinomial)
        }
      
      
      
        # Cumulative logit model for O2 -------------------------------------------------
        for (i in 1:100) {
          M_lvlone[i, 4] ~ dcat(p_O2[i, 1:4])
          eta_O2[i] <- (M_lvlone[i, 17] - spM_lvlone[17, 1])/spM_lvlone[17, 2] * alpha[24]
      
          p_O2[i, 1] <- 1 - max(1e-10, min(1-1e-10, sum(p_O2[i, 2:4])))
          p_O2[i, 2] <- max(1e-10, min(1-1e-10, psum_O2[i, 1] - psum_O2[i, 2]))
          p_O2[i, 3] <- max(1e-10, min(1-1e-10, psum_O2[i, 2] - psum_O2[i, 3]))
          p_O2[i, 4] <- max(1e-10, min(1-1e-10, psum_O2[i, 3]))
      
          logit(psum_O2[i, 1]) <- gamma_O2[1] + eta_O2[i]
          logit(psum_O2[i, 2]) <- gamma_O2[2] + eta_O2[i]
          logit(psum_O2[i, 3]) <- gamma_O2[3] + eta_O2[i]
      
          M_lvlone[i, 9] <- ifelse(M_lvlone[i, 4] == 2, 1, 0)
          M_lvlone[i, 10] <- ifelse(M_lvlone[i, 4] == 3, 1, 0)
          M_lvlone[i, 11] <- ifelse(M_lvlone[i, 4] == 4, 1, 0)
        }
      
        # Priors for the model for O2
        for (k in 24:24) {
          alpha[k] ~ dnorm(mu_reg_ordinal, tau_reg_ordinal)
        }
      
        delta_O2[1] ~ dnorm(mu_delta_ordinal, tau_delta_ordinal)
        delta_O2[2] ~ dnorm(mu_delta_ordinal, tau_delta_ordinal)
      
        gamma_O2[1] ~ dnorm(mu_delta_ordinal, tau_delta_ordinal)
        gamma_O2[2] <- gamma_O2[1] - exp(delta_O2[1])
        gamma_O2[3] <- gamma_O2[2] - exp(delta_O2[2]) 
       
        # Re-calculate interaction terms
        for (i in 1:100) {
          M_lvlone[i, 14] <- M_lvlone[i, 9] * M_lvlone[i, 12]
          M_lvlone[i, 15] <- M_lvlone[i, 10] * M_lvlone[i, 12]
          M_lvlone[i, 16] <- M_lvlone[i, 11] * M_lvlone[i, 12]
        }
      
       }
      $m4b
      model { 
      
         # Multinomial logit model for M1 ------------------------------------------------
        for (i in 1:100) {
          M_lvlone[i, 1] ~ dcat(p_M1[i, 1:4])
      
          p_M1[i, 1] <- min(1-1e-7, max(1e-7, phi_M1[i, 1] / sum(phi_M1[i, ])))
          p_M1[i, 2] <- min(1-1e-7, max(1e-7, phi_M1[i, 2] / sum(phi_M1[i, ])))
          p_M1[i, 3] <- min(1-1e-7, max(1e-7, phi_M1[i, 3] / sum(phi_M1[i, ])))
          p_M1[i, 4] <- min(1-1e-7, max(1e-7, phi_M1[i, 4] / sum(phi_M1[i, ])))
      
          log(phi_M1[i, 1]) <- 0
          log(phi_M1[i, 2]) <- M_lvlone[i, 4] * beta[1] +
                               (M_lvlone[i, 5] - spM_lvlone[5, 1])/spM_lvlone[5, 2] * beta[2] +
                               (M_lvlone[i, 6] - spM_lvlone[6, 1])/spM_lvlone[6, 2] * beta[3] +
                               (M_lvlone[i, 7] - spM_lvlone[7, 1])/spM_lvlone[7, 2] * beta[4] +
                               (M_lvlone[i, 8] - spM_lvlone[8, 1])/spM_lvlone[8, 2] * beta[5]
          log(phi_M1[i, 3]) <- M_lvlone[i, 4] * beta[6] +
                               (M_lvlone[i, 5] - spM_lvlone[5, 1])/spM_lvlone[5, 2] * beta[7] +
                               (M_lvlone[i, 6] - spM_lvlone[6, 1])/spM_lvlone[6, 2] * beta[8] +
                               (M_lvlone[i, 7] - spM_lvlone[7, 1])/spM_lvlone[7, 2] * beta[9] +
                               (M_lvlone[i, 8] - spM_lvlone[8, 1])/spM_lvlone[8, 2] * beta[10]
          log(phi_M1[i, 4]) <- M_lvlone[i, 4] * beta[11] +
                               (M_lvlone[i, 5] - spM_lvlone[5, 1])/spM_lvlone[5, 2] * beta[12] +
                               (M_lvlone[i, 6] - spM_lvlone[6, 1])/spM_lvlone[6, 2] * beta[13] +
                               (M_lvlone[i, 7] - spM_lvlone[7, 1])/spM_lvlone[7, 2] * beta[14] +
                               (M_lvlone[i, 8] - spM_lvlone[8, 1])/spM_lvlone[8, 2] * beta[15]
        }
      
        # Priors for the model for M1
        for (k in 1:15) {
          beta[k] ~ dnorm(mu_reg_multinomial, tau_reg_multinomial)
        }
      
      
      
        # Normal model for C2 -----------------------------------------------------------
        for (i in 1:100) {
          M_lvlone[i, 2] ~ dnorm(mu_C2[i], tau_C2)
          mu_C2[i] <- M_lvlone[i, 4] * alpha[1] + M_lvlone[i, 9] * alpha[2] +
                      M_lvlone[i, 10] * alpha[3] + M_lvlone[i, 11] * alpha[4] +
                      M_lvlone[i, 12] * alpha[5] + M_lvlone[i, 13] * alpha[6] +
                      M_lvlone[i, 14] * alpha[7] +
                      (M_lvlone[i, 15] - spM_lvlone[15, 1])/spM_lvlone[15, 2] * alpha[8]
      
          M_lvlone[i, 6] <- abs(M_lvlone[i, 15] - M_lvlone[i, 2])
      
      
        }
      
        # Priors for the model for C2
        for (k in 1:8) {
          alpha[k] ~ dnorm(mu_reg_norm, tau_reg_norm)
        }
        tau_C2 ~ dgamma(shape_tau_norm, rate_tau_norm)
        sigma_C2 <- sqrt(1/tau_C2)
      
      
      
        # Multinomial logit model for M2 ------------------------------------------------
        for (i in 1:100) {
          M_lvlone[i, 3] ~ dcat(p_M2[i, 1:4])
      
          p_M2[i, 1] <- min(1-1e-7, max(1e-7, phi_M2[i, 1] / sum(phi_M2[i, ])))
          p_M2[i, 2] <- min(1-1e-7, max(1e-7, phi_M2[i, 2] / sum(phi_M2[i, ])))
          p_M2[i, 3] <- min(1-1e-7, max(1e-7, phi_M2[i, 3] / sum(phi_M2[i, ])))
          p_M2[i, 4] <- min(1-1e-7, max(1e-7, phi_M2[i, 4] / sum(phi_M2[i, ])))
      
          log(phi_M2[i, 1]) <- 0
          log(phi_M2[i, 2]) <- M_lvlone[i, 4] * alpha[9] + M_lvlone[i, 12] * alpha[10] +
                               M_lvlone[i, 13] * alpha[11] + M_lvlone[i, 14] * alpha[12] +
                               (M_lvlone[i, 15] - spM_lvlone[15, 1])/spM_lvlone[15, 2] * alpha[13]
          log(phi_M2[i, 3]) <- M_lvlone[i, 4] * alpha[14] + M_lvlone[i, 12] * alpha[15] +
                               M_lvlone[i, 13] * alpha[16] + M_lvlone[i, 14] * alpha[17] +
                               (M_lvlone[i, 15] - spM_lvlone[15, 1])/spM_lvlone[15, 2] * alpha[18]
          log(phi_M2[i, 4]) <- M_lvlone[i, 4] * alpha[19] + M_lvlone[i, 12] * alpha[20] +
                               M_lvlone[i, 13] * alpha[21] + M_lvlone[i, 14] * alpha[22] +
                               (M_lvlone[i, 15] - spM_lvlone[15, 1])/spM_lvlone[15, 2] * alpha[23]
      
          M_lvlone[i, 9] <- ifelse(M_lvlone[i, 3] == 2, 1, 0)
          M_lvlone[i, 10] <- ifelse(M_lvlone[i, 3] == 3, 1, 0)
          M_lvlone[i, 11] <- ifelse(M_lvlone[i, 3] == 4, 1, 0)
      
      
      
          M_lvlone[i, 5] <- ifelse((M_lvlone[i, 3]) > (M_lvlone[i, 16]), 1, 0)
      
        }
      
        # Priors for the model for M2
        for (k in 9:23) {
          alpha[k] ~ dnorm(mu_reg_multinomial, tau_reg_multinomial)
        }
       
       
        # Re-calculate interaction terms
        for (i in 1:100) {
          M_lvlone[i, 8] <- M_lvlone[i, 5] * M_lvlone[i, 6]
        }
      
       }

# GRcrit and MCerror give same result

    Code
      lapply(models0, GR_crit, multivariate = FALSE)
    Output
      $m0a
      Potential scale reduction factors:
      
                       Point est. Upper C.I.
      M12: (Intercept)        NaN        NaN
      M13: (Intercept)        NaN        NaN
      M14: (Intercept)        NaN        NaN
      
      
      $m0b
      Potential scale reduction factors:
      
                       Point est. Upper C.I.
      M22: (Intercept)        NaN        NaN
      M23: (Intercept)        NaN        NaN
      M24: (Intercept)        NaN        NaN
      
      
      $m1a
      Potential scale reduction factors:
      
                       Point est. Upper C.I.
      M12: (Intercept)        NaN        NaN
      M12: C1                 NaN        NaN
      M13: (Intercept)        NaN        NaN
      M13: C1                 NaN        NaN
      M14: (Intercept)        NaN        NaN
      M14: C1                 NaN        NaN
      
      
      $m1b
      Potential scale reduction factors:
      
                       Point est. Upper C.I.
      M22: (Intercept)        NaN        NaN
      M22: C1                 NaN        NaN
      M23: (Intercept)        NaN        NaN
      M23: C1                 NaN        NaN
      M24: (Intercept)        NaN        NaN
      M24: C1                 NaN        NaN
      
      
      $m2a
      Potential scale reduction factors:
      
                       Point est. Upper C.I.
      M12: (Intercept)        NaN        NaN
      M12: C2                 NaN        NaN
      M13: (Intercept)        NaN        NaN
      M13: C2                 NaN        NaN
      M14: (Intercept)        NaN        NaN
      M14: C2                 NaN        NaN
      
      
      $m2b
      Potential scale reduction factors:
      
                       Point est. Upper C.I.
      M22: (Intercept)        NaN        NaN
      M22: C2                 NaN        NaN
      M23: (Intercept)        NaN        NaN
      M23: C2                 NaN        NaN
      M24: (Intercept)        NaN        NaN
      M24: C2                 NaN        NaN
      
      
      $m3a
      Potential scale reduction factors:
      
                  Point est. Upper C.I.
      (Intercept)        NaN        NaN
      M12                NaN        NaN
      M13                NaN        NaN
      M14                NaN        NaN
      sigma_C1           NaN        NaN
      
      
      $m3b
      Potential scale reduction factors:
      
                  Point est. Upper C.I.
      (Intercept)        NaN        NaN
      M22                NaN        NaN
      M23                NaN        NaN
      M24                NaN        NaN
      sigma_C1           NaN        NaN
      
      
      $m4a
      Potential scale reduction factors:
      
                            Point est. Upper C.I.
      M12: (Intercept)             NaN        NaN
      M12: M22                     NaN        NaN
      M12: M23                     NaN        NaN
      M12: M24                     NaN        NaN
      M12: O22                     NaN        NaN
      M12: O23                     NaN        NaN
      M12: O24                     NaN        NaN
      M12: abs(C1 - C2)            NaN        NaN
      M12: log(C1)                 NaN        NaN
      M12: O22:abs(C1 - C2)        NaN        NaN
      M12: O23:abs(C1 - C2)        NaN        NaN
      M12: O24:abs(C1 - C2)        NaN        NaN
      M13: (Intercept)             NaN        NaN
      M13: M22                     NaN        NaN
      M13: M23                     NaN        NaN
      M13: M24                     NaN        NaN
      M13: O22                     NaN        NaN
      M13: O23                     NaN        NaN
      M13: O24                     NaN        NaN
      M13: abs(C1 - C2)            NaN        NaN
      M13: log(C1)                 NaN        NaN
      M13: O22:abs(C1 - C2)        NaN        NaN
      M13: O23:abs(C1 - C2)        NaN        NaN
      M13: O24:abs(C1 - C2)        NaN        NaN
      M14: (Intercept)             NaN        NaN
      M14: M22                     NaN        NaN
      M14: M23                     NaN        NaN
      M14: M24                     NaN        NaN
      M14: O22                     NaN        NaN
      M14: O23                     NaN        NaN
      M14: O24                     NaN        NaN
      M14: abs(C1 - C2)            NaN        NaN
      M14: log(C1)                 NaN        NaN
      M14: O22:abs(C1 - C2)        NaN        NaN
      M14: O23:abs(C1 - C2)        NaN        NaN
      M14: O24:abs(C1 - C2)        NaN        NaN
      
      
      $m4b
      Potential scale reduction factors:
      
                                                                      Point est.
      M12: (Intercept)                                                       NaN
      M12: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                     NaN
      M12: abs(C1 - C2)                                                      NaN
      M12: log(C1)                                                           NaN
      M12: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)        NaN
      M13: (Intercept)                                                       NaN
      M13: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                     NaN
      M13: abs(C1 - C2)                                                      NaN
      M13: log(C1)                                                           NaN
      M13: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)        NaN
      M14: (Intercept)                                                       NaN
      M14: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                     NaN
      M14: abs(C1 - C2)                                                      NaN
      M14: log(C1)                                                           NaN
      M14: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)        NaN
                                                                      Upper C.I.
      M12: (Intercept)                                                       NaN
      M12: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                     NaN
      M12: abs(C1 - C2)                                                      NaN
      M12: log(C1)                                                           NaN
      M12: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)        NaN
      M13: (Intercept)                                                       NaN
      M13: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                     NaN
      M13: abs(C1 - C2)                                                      NaN
      M13: log(C1)                                                           NaN
      M13: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)        NaN
      M14: (Intercept)                                                       NaN
      M14: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                     NaN
      M14: abs(C1 - C2)                                                      NaN
      M14: log(C1)                                                           NaN
      M14: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)        NaN
      
      

---

    Code
      lapply(models0, MC_error)
    Output
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      $m0a
                       est MCSE SD MCSE/SD
      M12: (Intercept)   0    0  0     NaN
      M13: (Intercept)   0    0  0     NaN
      M14: (Intercept)   0    0  0     NaN
      
      $m0b
                       est MCSE SD MCSE/SD
      M22: (Intercept)   0    0  0     NaN
      M23: (Intercept)   0    0  0     NaN
      M24: (Intercept)   0    0  0     NaN
      
      $m1a
                       est MCSE SD MCSE/SD
      M12: (Intercept)   0    0  0     NaN
      M12: C1            0    0  0     NaN
      M13: (Intercept)   0    0  0     NaN
      M13: C1            0    0  0     NaN
      M14: (Intercept)   0    0  0     NaN
      M14: C1            0    0  0     NaN
      
      $m1b
                       est MCSE SD MCSE/SD
      M22: (Intercept)   0    0  0     NaN
      M22: C1            0    0  0     NaN
      M23: (Intercept)   0    0  0     NaN
      M23: C1            0    0  0     NaN
      M24: (Intercept)   0    0  0     NaN
      M24: C1            0    0  0     NaN
      
      $m2a
                       est MCSE SD MCSE/SD
      M12: (Intercept)   0    0  0     NaN
      M12: C2            0    0  0     NaN
      M13: (Intercept)   0    0  0     NaN
      M13: C2            0    0  0     NaN
      M14: (Intercept)   0    0  0     NaN
      M14: C2            0    0  0     NaN
      
      $m2b
                       est MCSE SD MCSE/SD
      M22: (Intercept)   0    0  0     NaN
      M22: C2            0    0  0     NaN
      M23: (Intercept)   0    0  0     NaN
      M23: C2            0    0  0     NaN
      M24: (Intercept)   0    0  0     NaN
      M24: C2            0    0  0     NaN
      
      $m3a
                  est MCSE SD MCSE/SD
      (Intercept)   0    0  0     NaN
      M12           0    0  0     NaN
      M13           0    0  0     NaN
      M14           0    0  0     NaN
      sigma_C1      0    0  0     NaN
      
      $m3b
                  est MCSE SD MCSE/SD
      (Intercept)   0    0  0     NaN
      M22           0    0  0     NaN
      M23           0    0  0     NaN
      M24           0    0  0     NaN
      sigma_C1      0    0  0     NaN
      
      $m4a
                            est MCSE SD MCSE/SD
      M12: (Intercept)        0    0  0     NaN
      M12: M22                0    0  0     NaN
      M12: M23                0    0  0     NaN
      M12: M24                0    0  0     NaN
      M12: O22                0    0  0     NaN
      M12: O23                0    0  0     NaN
      M12: O24                0    0  0     NaN
      M12: abs(C1 - C2)       0    0  0     NaN
      M12: log(C1)            0    0  0     NaN
      M12: O22:abs(C1 - C2)   0    0  0     NaN
      M12: O23:abs(C1 - C2)   0    0  0     NaN
      M12: O24:abs(C1 - C2)   0    0  0     NaN
      M13: (Intercept)        0    0  0     NaN
      M13: M22                0    0  0     NaN
      M13: M23                0    0  0     NaN
      M13: M24                0    0  0     NaN
      M13: O22                0    0  0     NaN
      M13: O23                0    0  0     NaN
      M13: O24                0    0  0     NaN
      M13: abs(C1 - C2)       0    0  0     NaN
      M13: log(C1)            0    0  0     NaN
      M13: O22:abs(C1 - C2)   0    0  0     NaN
      M13: O23:abs(C1 - C2)   0    0  0     NaN
      M13: O24:abs(C1 - C2)   0    0  0     NaN
      M14: (Intercept)        0    0  0     NaN
      M14: M22                0    0  0     NaN
      M14: M23                0    0  0     NaN
      M14: M24                0    0  0     NaN
      M14: O22                0    0  0     NaN
      M14: O23                0    0  0     NaN
      M14: O24                0    0  0     NaN
      M14: abs(C1 - C2)       0    0  0     NaN
      M14: log(C1)            0    0  0     NaN
      M14: O22:abs(C1 - C2)   0    0  0     NaN
      M14: O23:abs(C1 - C2)   0    0  0     NaN
      M14: O24:abs(C1 - C2)   0    0  0     NaN
      
      $m4b
                                                                      est MCSE SD
      M12: (Intercept)                                                  0    0  0
      M12: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                0    0  0
      M12: abs(C1 - C2)                                                 0    0  0
      M12: log(C1)                                                      0    0  0
      M12: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)   0    0  0
      M13: (Intercept)                                                  0    0  0
      M13: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                0    0  0
      M13: abs(C1 - C2)                                                 0    0  0
      M13: log(C1)                                                      0    0  0
      M13: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)   0    0  0
      M14: (Intercept)                                                  0    0  0
      M14: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                0    0  0
      M14: abs(C1 - C2)                                                 0    0  0
      M14: log(C1)                                                      0    0  0
      M14: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)   0    0  0
                                                                      MCSE/SD
      M12: (Intercept)                                                    NaN
      M12: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                  NaN
      M12: abs(C1 - C2)                                                   NaN
      M12: log(C1)                                                        NaN
      M12: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)     NaN
      M13: (Intercept)                                                    NaN
      M13: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                  NaN
      M13: abs(C1 - C2)                                                   NaN
      M13: log(C1)                                                        NaN
      M13: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)     NaN
      M14: (Intercept)                                                    NaN
      M14: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                  NaN
      M14: abs(C1 - C2)                                                   NaN
      M14: log(C1)                                                        NaN
      M14: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)     NaN
      

# summary output remained the same

    Code
      lapply(models0, print)
    Output
      
      Call:
      mlogit_imp(formula = M1 ~ 1, data = wideDF, n.adapt = 5, n.iter = 10, 
          seed = 2020, warn = FALSE, mess = FALSE)
      
       Bayesian multinomial logit model for "M1" 
      
      
      Coefficients:
      (Intercept) (Intercept) (Intercept) 
                0           0           0 
      
      Call:
      mlogit_imp(formula = M2 ~ 1, data = wideDF, n.adapt = 5, n.iter = 10, 
          seed = 2020, warn = FALSE, mess = FALSE)
      
       Bayesian multinomial logit model for "M2" 
      
      
      Coefficients:
      (Intercept) (Intercept) (Intercept) 
                0           0           0 
      
      Call:
      mlogit_imp(formula = M1 ~ C1, data = wideDF, n.adapt = 5, n.iter = 10, 
          seed = 2020, warn = FALSE, mess = FALSE)
      
       Bayesian multinomial logit model for "M1" 
      
      
      Coefficients:
      (Intercept)          C1 (Intercept)          C1 (Intercept)          C1 
                0           0           0           0           0           0 
      
      Call:
      mlogit_imp(formula = M2 ~ C1, data = wideDF, n.adapt = 5, n.iter = 10, 
          seed = 2020, warn = FALSE, mess = FALSE)
      
       Bayesian multinomial logit model for "M2" 
      
      
      Coefficients:
      (Intercept)          C1 (Intercept)          C1 (Intercept)          C1 
                0           0           0           0           0           0 
      
      Call:
      mlogit_imp(formula = M1 ~ C2, data = wideDF, n.adapt = 5, n.iter = 10, 
          seed = 2020, warn = FALSE, mess = FALSE)
      
       Bayesian multinomial logit model for "M1" 
      
      
      Coefficients:
      (Intercept)          C2 (Intercept)          C2 (Intercept)          C2 
                0           0           0           0           0           0 
      
      Call:
      mlogit_imp(formula = M2 ~ C2, data = wideDF, n.adapt = 5, n.iter = 10, 
          seed = 2020, warn = FALSE, mess = FALSE)
      
       Bayesian multinomial logit model for "M2" 
      
      
      Coefficients:
      (Intercept)          C2 (Intercept)          C2 (Intercept)          C2 
                0           0           0           0           0           0 
      
      Call:
      lm_imp(formula = C1 ~ M1, data = wideDF, n.adapt = 5, n.iter = 10, 
          seed = 2020, warn = FALSE, mess = FALSE)
      
       Bayesian linear model for "C1" 
      
      
      Coefficients:
      (Intercept)         M12         M13         M14 
                0           0           0           0 
      
      
      Residual standard deviation:
      sigma_C1 
             0 
      
      Call:
      lm_imp(formula = C1 ~ M2, data = wideDF, n.adapt = 5, n.iter = 10, 
          seed = 2020, warn = FALSE, mess = FALSE)
      
       Bayesian linear model for "C1" 
      
      
      Coefficients:
      (Intercept)         M22         M23         M24 
                0           0           0           0 
      
      
      Residual standard deviation:
      sigma_C1 
             0 
      
      Call:
      mlogit_imp(formula = M1 ~ M2 + O2 * abs(C1 - C2) + log(C1), data = wideDF, 
          n.adapt = 5, n.iter = 10, monitor_params = list(other = "p_M1"), 
          seed = 2020, warn = FALSE, mess = FALSE)
      
       Bayesian multinomial logit model for "M1" 
      
      
      Coefficients:
           (Intercept)              M22              M23              M24 
                     0                0                0                0 
                   O22              O23              O24     abs(C1 - C2) 
                     0                0                0                0 
               log(C1) O22:abs(C1 - C2) O23:abs(C1 - C2) O24:abs(C1 - C2) 
                     0                0                0                0 
           (Intercept)              M22              M23              M24 
                     0                0                0                0 
                   O22              O23              O24     abs(C1 - C2) 
                     0                0                0                0 
               log(C1) O22:abs(C1 - C2) O23:abs(C1 - C2) O24:abs(C1 - C2) 
                     0                0                0                0 
           (Intercept)              M22              M23              M24 
                     0                0                0                0 
                   O22              O23              O24     abs(C1 - C2) 
                     0                0                0                0 
               log(C1) O22:abs(C1 - C2) O23:abs(C1 - C2) O24:abs(C1 - C2) 
                     0                0                0                0 
      
      Call:
      mlogit_imp(formula = M1 ~ ifelse(as.numeric(M2) > as.numeric(O1), 
          1, 0) * abs(C1 - C2) + log(C1), data = wideDF, n.adapt = 5, 
          n.iter = 10, monitor_params = list(other = "p_M1"), seed = 2020, 
          warn = FALSE, mess = FALSE)
      
       Bayesian multinomial logit model for "M1" 
      
      
      Coefficients:
                                                     (Intercept) 
                                                               0 
                   ifelse(as.numeric(M2) > as.numeric(O1), 1, 0) 
                                                               0 
                                                    abs(C1 - C2) 
                                                               0 
                                                         log(C1) 
                                                               0 
      ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2) 
                                                               0 
                                                     (Intercept) 
                                                               0 
                   ifelse(as.numeric(M2) > as.numeric(O1), 1, 0) 
                                                               0 
                                                    abs(C1 - C2) 
                                                               0 
                                                         log(C1) 
                                                               0 
      ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2) 
                                                               0 
                                                     (Intercept) 
                                                               0 
                   ifelse(as.numeric(M2) > as.numeric(O1), 1, 0) 
                                                               0 
                                                    abs(C1 - C2) 
                                                               0 
                                                         log(C1) 
                                                               0 
      ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2) 
                                                               0 
      $m0a
      
      Call:
      mlogit_imp(formula = M1 ~ 1, data = wideDF, n.adapt = 5, n.iter = 10, 
          seed = 2020, warn = FALSE, mess = FALSE)
      
       Bayesian multinomial logit model for "M1" 
      
      
      Coefficients:
      (Intercept) (Intercept) (Intercept) 
                0           0           0 
      
      $m0b
      
      Call:
      mlogit_imp(formula = M2 ~ 1, data = wideDF, n.adapt = 5, n.iter = 10, 
          seed = 2020, warn = FALSE, mess = FALSE)
      
       Bayesian multinomial logit model for "M2" 
      
      
      Coefficients:
      (Intercept) (Intercept) (Intercept) 
                0           0           0 
      
      $m1a
      
      Call:
      mlogit_imp(formula = M1 ~ C1, data = wideDF, n.adapt = 5, n.iter = 10, 
          seed = 2020, warn = FALSE, mess = FALSE)
      
       Bayesian multinomial logit model for "M1" 
      
      
      Coefficients:
      (Intercept)          C1 (Intercept)          C1 (Intercept)          C1 
                0           0           0           0           0           0 
      
      $m1b
      
      Call:
      mlogit_imp(formula = M2 ~ C1, data = wideDF, n.adapt = 5, n.iter = 10, 
          seed = 2020, warn = FALSE, mess = FALSE)
      
       Bayesian multinomial logit model for "M2" 
      
      
      Coefficients:
      (Intercept)          C1 (Intercept)          C1 (Intercept)          C1 
                0           0           0           0           0           0 
      
      $m2a
      
      Call:
      mlogit_imp(formula = M1 ~ C2, data = wideDF, n.adapt = 5, n.iter = 10, 
          seed = 2020, warn = FALSE, mess = FALSE)
      
       Bayesian multinomial logit model for "M1" 
      
      
      Coefficients:
      (Intercept)          C2 (Intercept)          C2 (Intercept)          C2 
                0           0           0           0           0           0 
      
      $m2b
      
      Call:
      mlogit_imp(formula = M2 ~ C2, data = wideDF, n.adapt = 5, n.iter = 10, 
          seed = 2020, warn = FALSE, mess = FALSE)
      
       Bayesian multinomial logit model for "M2" 
      
      
      Coefficients:
      (Intercept)          C2 (Intercept)          C2 (Intercept)          C2 
                0           0           0           0           0           0 
      
      $m3a
      
      Call:
      lm_imp(formula = C1 ~ M1, data = wideDF, n.adapt = 5, n.iter = 10, 
          seed = 2020, warn = FALSE, mess = FALSE)
      
       Bayesian linear model for "C1" 
      
      
      Coefficients:
      (Intercept)         M12         M13         M14 
                0           0           0           0 
      
      
      Residual standard deviation:
      sigma_C1 
             0 
      
      $m3b
      
      Call:
      lm_imp(formula = C1 ~ M2, data = wideDF, n.adapt = 5, n.iter = 10, 
          seed = 2020, warn = FALSE, mess = FALSE)
      
       Bayesian linear model for "C1" 
      
      
      Coefficients:
      (Intercept)         M22         M23         M24 
                0           0           0           0 
      
      
      Residual standard deviation:
      sigma_C1 
             0 
      
      $m4a
      
      Call:
      mlogit_imp(formula = M1 ~ M2 + O2 * abs(C1 - C2) + log(C1), data = wideDF, 
          n.adapt = 5, n.iter = 10, monitor_params = list(other = "p_M1"), 
          seed = 2020, warn = FALSE, mess = FALSE)
      
       Bayesian multinomial logit model for "M1" 
      
      
      Coefficients:
           (Intercept)              M22              M23              M24 
                     0                0                0                0 
                   O22              O23              O24     abs(C1 - C2) 
                     0                0                0                0 
               log(C1) O22:abs(C1 - C2) O23:abs(C1 - C2) O24:abs(C1 - C2) 
                     0                0                0                0 
           (Intercept)              M22              M23              M24 
                     0                0                0                0 
                   O22              O23              O24     abs(C1 - C2) 
                     0                0                0                0 
               log(C1) O22:abs(C1 - C2) O23:abs(C1 - C2) O24:abs(C1 - C2) 
                     0                0                0                0 
           (Intercept)              M22              M23              M24 
                     0                0                0                0 
                   O22              O23              O24     abs(C1 - C2) 
                     0                0                0                0 
               log(C1) O22:abs(C1 - C2) O23:abs(C1 - C2) O24:abs(C1 - C2) 
                     0                0                0                0 
      
      $m4b
      
      Call:
      mlogit_imp(formula = M1 ~ ifelse(as.numeric(M2) > as.numeric(O1), 
          1, 0) * abs(C1 - C2) + log(C1), data = wideDF, n.adapt = 5, 
          n.iter = 10, monitor_params = list(other = "p_M1"), seed = 2020, 
          warn = FALSE, mess = FALSE)
      
       Bayesian multinomial logit model for "M1" 
      
      
      Coefficients:
                                                     (Intercept) 
                                                               0 
                   ifelse(as.numeric(M2) > as.numeric(O1), 1, 0) 
                                                               0 
                                                    abs(C1 - C2) 
                                                               0 
                                                         log(C1) 
                                                               0 
      ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2) 
                                                               0 
                                                     (Intercept) 
                                                               0 
                   ifelse(as.numeric(M2) > as.numeric(O1), 1, 0) 
                                                               0 
                                                    abs(C1 - C2) 
                                                               0 
                                                         log(C1) 
                                                               0 
      ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2) 
                                                               0 
                                                     (Intercept) 
                                                               0 
                   ifelse(as.numeric(M2) > as.numeric(O1), 1, 0) 
                                                               0 
                                                    abs(C1 - C2) 
                                                               0 
                                                         log(C1) 
                                                               0 
      ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2) 
                                                               0 
      

---

    Code
      lapply(models0, coef)
    Output
      $m0a
      $m0a$M1
      (Intercept) (Intercept) (Intercept) 
                0           0           0 
      
      
      $m0b
      $m0b$M2
      (Intercept) (Intercept) (Intercept) 
                0           0           0 
      
      
      $m1a
      $m1a$M1
      (Intercept)          C1 (Intercept)          C1 (Intercept)          C1 
                0           0           0           0           0           0 
      
      
      $m1b
      $m1b$M2
      (Intercept)          C1 (Intercept)          C1 (Intercept)          C1 
                0           0           0           0           0           0 
      
      
      $m2a
      $m2a$M1
      (Intercept)          C2 (Intercept)          C2 (Intercept)          C2 
                0           0           0           0           0           0 
      
      
      $m2b
      $m2b$M2
      (Intercept)          C2 (Intercept)          C2 (Intercept)          C2 
                0           0           0           0           0           0 
      
      
      $m3a
      $m3a$C1
      (Intercept)         M12         M13         M14    sigma_C1 
                0           0           0           0           0 
      
      
      $m3b
      $m3b$C1
      (Intercept)         M22         M23         M24    sigma_C1 
                0           0           0           0           0 
      
      
      $m4a
      $m4a$M1
           (Intercept)              M22              M23              M24 
                     0                0                0                0 
                   O22              O23              O24     abs(C1 - C2) 
                     0                0                0                0 
               log(C1) O22:abs(C1 - C2) O23:abs(C1 - C2) O24:abs(C1 - C2) 
                     0                0                0                0 
           (Intercept)              M22              M23              M24 
                     0                0                0                0 
                   O22              O23              O24     abs(C1 - C2) 
                     0                0                0                0 
               log(C1) O22:abs(C1 - C2) O23:abs(C1 - C2) O24:abs(C1 - C2) 
                     0                0                0                0 
           (Intercept)              M22              M23              M24 
                     0                0                0                0 
                   O22              O23              O24     abs(C1 - C2) 
                     0                0                0                0 
               log(C1) O22:abs(C1 - C2) O23:abs(C1 - C2) O24:abs(C1 - C2) 
                     0                0                0                0 
      
      
      $m4b
      $m4b$M1
                                                     (Intercept) 
                                                               0 
                   ifelse(as.numeric(M2) > as.numeric(O1), 1, 0) 
                                                               0 
                                                    abs(C1 - C2) 
                                                               0 
                                                         log(C1) 
                                                               0 
      ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2) 
                                                               0 
                                                     (Intercept) 
                                                               0 
                   ifelse(as.numeric(M2) > as.numeric(O1), 1, 0) 
                                                               0 
                                                    abs(C1 - C2) 
                                                               0 
                                                         log(C1) 
                                                               0 
      ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2) 
                                                               0 
                                                     (Intercept) 
                                                               0 
                   ifelse(as.numeric(M2) > as.numeric(O1), 1, 0) 
                                                               0 
                                                    abs(C1 - C2) 
                                                               0 
                                                         log(C1) 
                                                               0 
      ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2) 
                                                               0 
      
      

---

    Code
      lapply(models0, confint)
    Output
      $m0a
      $m0a$M1
                  2.5% 97.5%
      (Intercept)    0     0
      (Intercept)    0     0
      (Intercept)    0     0
      
      
      $m0b
      $m0b$M2
                  2.5% 97.5%
      (Intercept)    0     0
      (Intercept)    0     0
      (Intercept)    0     0
      
      
      $m1a
      $m1a$M1
                  2.5% 97.5%
      (Intercept)    0     0
      C1             0     0
      (Intercept)    0     0
      C1             0     0
      (Intercept)    0     0
      C1             0     0
      
      
      $m1b
      $m1b$M2
                  2.5% 97.5%
      (Intercept)    0     0
      C1             0     0
      (Intercept)    0     0
      C1             0     0
      (Intercept)    0     0
      C1             0     0
      
      
      $m2a
      $m2a$M1
                  2.5% 97.5%
      (Intercept)    0     0
      C2             0     0
      (Intercept)    0     0
      C2             0     0
      (Intercept)    0     0
      C2             0     0
      
      
      $m2b
      $m2b$M2
                  2.5% 97.5%
      (Intercept)    0     0
      C2             0     0
      (Intercept)    0     0
      C2             0     0
      (Intercept)    0     0
      C2             0     0
      
      
      $m3a
      $m3a$C1
                  2.5% 97.5%
      (Intercept)    0     0
      M12            0     0
      M13            0     0
      M14            0     0
      sigma_C1       0     0
      
      
      $m3b
      $m3b$C1
                  2.5% 97.5%
      (Intercept)    0     0
      M22            0     0
      M23            0     0
      M24            0     0
      sigma_C1       0     0
      
      
      $m4a
      $m4a$M1
                       2.5% 97.5%
      (Intercept)         0     0
      M22                 0     0
      M23                 0     0
      M24                 0     0
      O22                 0     0
      O23                 0     0
      O24                 0     0
      abs(C1 - C2)        0     0
      log(C1)             0     0
      O22:abs(C1 - C2)    0     0
      O23:abs(C1 - C2)    0     0
      O24:abs(C1 - C2)    0     0
      (Intercept)         0     0
      M22                 0     0
      M23                 0     0
      M24                 0     0
      O22                 0     0
      O23                 0     0
      O24                 0     0
      abs(C1 - C2)        0     0
      log(C1)             0     0
      O22:abs(C1 - C2)    0     0
      O23:abs(C1 - C2)    0     0
      O24:abs(C1 - C2)    0     0
      (Intercept)         0     0
      M22                 0     0
      M23                 0     0
      M24                 0     0
      O22                 0     0
      O23                 0     0
      O24                 0     0
      abs(C1 - C2)        0     0
      log(C1)             0     0
      O22:abs(C1 - C2)    0     0
      O23:abs(C1 - C2)    0     0
      O24:abs(C1 - C2)    0     0
      
      
      $m4b
      $m4b$M1
                                                                 2.5% 97.5%
      (Intercept)                                                   0     0
      ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                 0     0
      abs(C1 - C2)                                                  0     0
      log(C1)                                                       0     0
      ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)    0     0
      (Intercept)                                                   0     0
      ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                 0     0
      abs(C1 - C2)                                                  0     0
      log(C1)                                                       0     0
      ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)    0     0
      (Intercept)                                                   0     0
      ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                 0     0
      abs(C1 - C2)                                                  0     0
      log(C1)                                                       0     0
      ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)    0     0
      
      

---

    Code
      lapply(models0, summary)
    Output
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      $m0a
      
      Bayesian multinomial logit model fitted with JointAI
      
      Call:
      mlogit_imp(formula = M1 ~ 1, data = wideDF, n.adapt = 5, n.iter = 10, 
          seed = 2020, warn = FALSE, mess = FALSE)
      
      
      Posterior summary:
                       Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
      M12: (Intercept)    0  0    0     0          0     NaN    NaN
      M13: (Intercept)    0  0    0     0          0     NaN    NaN
      M14: (Intercept)    0  0    0     0          0     NaN    NaN
      
      
      MCMC settings:
      Iterations = 6:15
      Sample size per chain = 10 
      Thinning interval = 1 
      Number of chains = 3 
      
      Number of observations: 100 
      
      $m0b
      
      Bayesian multinomial logit model fitted with JointAI
      
      Call:
      mlogit_imp(formula = M2 ~ 1, data = wideDF, n.adapt = 5, n.iter = 10, 
          seed = 2020, warn = FALSE, mess = FALSE)
      
      
      Posterior summary:
                       Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
      M22: (Intercept)    0  0    0     0          0     NaN    NaN
      M23: (Intercept)    0  0    0     0          0     NaN    NaN
      M24: (Intercept)    0  0    0     0          0     NaN    NaN
      
      
      MCMC settings:
      Iterations = 6:15
      Sample size per chain = 10 
      Thinning interval = 1 
      Number of chains = 3 
      
      Number of observations: 100 
      
      $m1a
      
      Bayesian multinomial logit model fitted with JointAI
      
      Call:
      mlogit_imp(formula = M1 ~ C1, data = wideDF, n.adapt = 5, n.iter = 10, 
          seed = 2020, warn = FALSE, mess = FALSE)
      
      
      Posterior summary:
                       Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
      M12: (Intercept)    0  0    0     0          0     NaN    NaN
      M12: C1             0  0    0     0          0     NaN    NaN
      M13: (Intercept)    0  0    0     0          0     NaN    NaN
      M13: C1             0  0    0     0          0     NaN    NaN
      M14: (Intercept)    0  0    0     0          0     NaN    NaN
      M14: C1             0  0    0     0          0     NaN    NaN
      
      
      MCMC settings:
      Iterations = 6:15
      Sample size per chain = 10 
      Thinning interval = 1 
      Number of chains = 3 
      
      Number of observations: 100 
      
      $m1b
      
      Bayesian multinomial logit model fitted with JointAI
      
      Call:
      mlogit_imp(formula = M2 ~ C1, data = wideDF, n.adapt = 5, n.iter = 10, 
          seed = 2020, warn = FALSE, mess = FALSE)
      
      
      Posterior summary:
                       Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
      M22: (Intercept)    0  0    0     0          0     NaN    NaN
      M22: C1             0  0    0     0          0     NaN    NaN
      M23: (Intercept)    0  0    0     0          0     NaN    NaN
      M23: C1             0  0    0     0          0     NaN    NaN
      M24: (Intercept)    0  0    0     0          0     NaN    NaN
      M24: C1             0  0    0     0          0     NaN    NaN
      
      
      MCMC settings:
      Iterations = 6:15
      Sample size per chain = 10 
      Thinning interval = 1 
      Number of chains = 3 
      
      Number of observations: 100 
      
      $m2a
      
      Bayesian multinomial logit model fitted with JointAI
      
      Call:
      mlogit_imp(formula = M1 ~ C2, data = wideDF, n.adapt = 5, n.iter = 10, 
          seed = 2020, warn = FALSE, mess = FALSE)
      
      
      Posterior summary:
                       Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
      M12: (Intercept)    0  0    0     0          0     NaN    NaN
      M12: C2             0  0    0     0          0     NaN    NaN
      M13: (Intercept)    0  0    0     0          0     NaN    NaN
      M13: C2             0  0    0     0          0     NaN    NaN
      M14: (Intercept)    0  0    0     0          0     NaN    NaN
      M14: C2             0  0    0     0          0     NaN    NaN
      
      
      MCMC settings:
      Iterations = 6:15
      Sample size per chain = 10 
      Thinning interval = 1 
      Number of chains = 3 
      
      Number of observations: 100 
      
      $m2b
      
      Bayesian multinomial logit model fitted with JointAI
      
      Call:
      mlogit_imp(formula = M2 ~ C2, data = wideDF, n.adapt = 5, n.iter = 10, 
          seed = 2020, warn = FALSE, mess = FALSE)
      
      
      Posterior summary:
                       Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
      M22: (Intercept)    0  0    0     0          0     NaN    NaN
      M22: C2             0  0    0     0          0     NaN    NaN
      M23: (Intercept)    0  0    0     0          0     NaN    NaN
      M23: C2             0  0    0     0          0     NaN    NaN
      M24: (Intercept)    0  0    0     0          0     NaN    NaN
      M24: C2             0  0    0     0          0     NaN    NaN
      
      
      MCMC settings:
      Iterations = 6:15
      Sample size per chain = 10 
      Thinning interval = 1 
      Number of chains = 3 
      
      Number of observations: 100 
      
      $m3a
      
      Bayesian linear model fitted with JointAI
      
      Call:
      lm_imp(formula = C1 ~ M1, data = wideDF, n.adapt = 5, n.iter = 10, 
          seed = 2020, warn = FALSE, mess = FALSE)
      
      
      Posterior summary:
                  Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
      (Intercept)    0  0    0     0          0     NaN    NaN
      M12            0  0    0     0          0     NaN    NaN
      M13            0  0    0     0          0     NaN    NaN
      M14            0  0    0     0          0     NaN    NaN
      
      Posterior summary of residual std. deviation:
               Mean SD 2.5% 97.5% GR-crit MCE/SD
      sigma_C1    0  0    0     0     NaN    NaN
      
      
      MCMC settings:
      Iterations = 1:10
      Sample size per chain = 10 
      Thinning interval = 1 
      Number of chains = 3 
      
      Number of observations: 100 
      
      $m3b
      
      Bayesian linear model fitted with JointAI
      
      Call:
      lm_imp(formula = C1 ~ M2, data = wideDF, n.adapt = 5, n.iter = 10, 
          seed = 2020, warn = FALSE, mess = FALSE)
      
      
      Posterior summary:
                  Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
      (Intercept)    0  0    0     0          0     NaN    NaN
      M22            0  0    0     0          0     NaN    NaN
      M23            0  0    0     0          0     NaN    NaN
      M24            0  0    0     0          0     NaN    NaN
      
      Posterior summary of residual std. deviation:
               Mean SD 2.5% 97.5% GR-crit MCE/SD
      sigma_C1    0  0    0     0     NaN    NaN
      
      
      MCMC settings:
      Iterations = 6:15
      Sample size per chain = 10 
      Thinning interval = 1 
      Number of chains = 3 
      
      Number of observations: 100 
      
      $m4a
      
      Bayesian multinomial logit model fitted with JointAI
      
      Call:
      mlogit_imp(formula = M1 ~ M2 + O2 * abs(C1 - C2) + log(C1), data = wideDF, 
          n.adapt = 5, n.iter = 10, monitor_params = list(other = "p_M1"), 
          seed = 2020, warn = FALSE, mess = FALSE)
      
      
      Posterior summary:
                            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
      M12: (Intercept)         0  0    0     0          0     NaN    NaN
      M12: M22                 0  0    0     0          0     NaN    NaN
      M12: M23                 0  0    0     0          0     NaN    NaN
      M12: M24                 0  0    0     0          0     NaN    NaN
      M12: O22                 0  0    0     0          0     NaN    NaN
      M12: O23                 0  0    0     0          0     NaN    NaN
      M12: O24                 0  0    0     0          0     NaN    NaN
      M12: abs(C1 - C2)        0  0    0     0          0     NaN    NaN
      M12: log(C1)             0  0    0     0          0     NaN    NaN
      M12: O22:abs(C1 - C2)    0  0    0     0          0     NaN    NaN
      M12: O23:abs(C1 - C2)    0  0    0     0          0     NaN    NaN
      M12: O24:abs(C1 - C2)    0  0    0     0          0     NaN    NaN
      M13: (Intercept)         0  0    0     0          0     NaN    NaN
      M13: M22                 0  0    0     0          0     NaN    NaN
      M13: M23                 0  0    0     0          0     NaN    NaN
      M13: M24                 0  0    0     0          0     NaN    NaN
      M13: O22                 0  0    0     0          0     NaN    NaN
      M13: O23                 0  0    0     0          0     NaN    NaN
      M13: O24                 0  0    0     0          0     NaN    NaN
      M13: abs(C1 - C2)        0  0    0     0          0     NaN    NaN
      M13: log(C1)             0  0    0     0          0     NaN    NaN
      M13: O22:abs(C1 - C2)    0  0    0     0          0     NaN    NaN
      M13: O23:abs(C1 - C2)    0  0    0     0          0     NaN    NaN
      M13: O24:abs(C1 - C2)    0  0    0     0          0     NaN    NaN
      M14: (Intercept)         0  0    0     0          0     NaN    NaN
      M14: M22                 0  0    0     0          0     NaN    NaN
      M14: M23                 0  0    0     0          0     NaN    NaN
      M14: M24                 0  0    0     0          0     NaN    NaN
      M14: O22                 0  0    0     0          0     NaN    NaN
      M14: O23                 0  0    0     0          0     NaN    NaN
      M14: O24                 0  0    0     0          0     NaN    NaN
      M14: abs(C1 - C2)        0  0    0     0          0     NaN    NaN
      M14: log(C1)             0  0    0     0          0     NaN    NaN
      M14: O22:abs(C1 - C2)    0  0    0     0          0     NaN    NaN
      M14: O23:abs(C1 - C2)    0  0    0     0          0     NaN    NaN
      M14: O24:abs(C1 - C2)    0  0    0     0          0     NaN    NaN
      
      
      MCMC settings:
      Iterations = 6:15
      Sample size per chain = 10 
      Thinning interval = 1 
      Number of chains = 3 
      
      Number of observations: 100 
      
      $m4b
      
      Bayesian multinomial logit model fitted with JointAI
      
      Call:
      mlogit_imp(formula = M1 ~ ifelse(as.numeric(M2) > as.numeric(O1), 
          1, 0) * abs(C1 - C2) + log(C1), data = wideDF, n.adapt = 5, 
          n.iter = 10, monitor_params = list(other = "p_M1"), seed = 2020, 
          warn = FALSE, mess = FALSE)
      
      
      Posterior summary:
                                                                      Mean SD 2.5%
      M12: (Intercept)                                                   0  0    0
      M12: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                 0  0    0
      M12: abs(C1 - C2)                                                  0  0    0
      M12: log(C1)                                                       0  0    0
      M12: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)    0  0    0
      M13: (Intercept)                                                   0  0    0
      M13: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                 0  0    0
      M13: abs(C1 - C2)                                                  0  0    0
      M13: log(C1)                                                       0  0    0
      M13: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)    0  0    0
      M14: (Intercept)                                                   0  0    0
      M14: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                 0  0    0
      M14: abs(C1 - C2)                                                  0  0    0
      M14: log(C1)                                                       0  0    0
      M14: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)    0  0    0
                                                                      97.5%
      M12: (Intercept)                                                    0
      M12: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                  0
      M12: abs(C1 - C2)                                                   0
      M12: log(C1)                                                        0
      M12: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)     0
      M13: (Intercept)                                                    0
      M13: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                  0
      M13: abs(C1 - C2)                                                   0
      M13: log(C1)                                                        0
      M13: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)     0
      M14: (Intercept)                                                    0
      M14: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                  0
      M14: abs(C1 - C2)                                                   0
      M14: log(C1)                                                        0
      M14: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)     0
                                                                      tail-prob.
      M12: (Intercept)                                                         0
      M12: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                       0
      M12: abs(C1 - C2)                                                        0
      M12: log(C1)                                                             0
      M12: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)          0
      M13: (Intercept)                                                         0
      M13: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                       0
      M13: abs(C1 - C2)                                                        0
      M13: log(C1)                                                             0
      M13: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)          0
      M14: (Intercept)                                                         0
      M14: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                       0
      M14: abs(C1 - C2)                                                        0
      M14: log(C1)                                                             0
      M14: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)          0
                                                                      GR-crit MCE/SD
      M12: (Intercept)                                                    NaN    NaN
      M12: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                  NaN    NaN
      M12: abs(C1 - C2)                                                   NaN    NaN
      M12: log(C1)                                                        NaN    NaN
      M12: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)     NaN    NaN
      M13: (Intercept)                                                    NaN    NaN
      M13: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                  NaN    NaN
      M13: abs(C1 - C2)                                                   NaN    NaN
      M13: log(C1)                                                        NaN    NaN
      M13: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)     NaN    NaN
      M14: (Intercept)                                                    NaN    NaN
      M14: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                  NaN    NaN
      M14: abs(C1 - C2)                                                   NaN    NaN
      M14: log(C1)                                                        NaN    NaN
      M14: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)     NaN    NaN
      
      
      MCMC settings:
      Iterations = 6:15
      Sample size per chain = 10 
      Thinning interval = 1 
      Number of chains = 3 
      
      Number of observations: 100 
      

---

    Code
      lapply(models0, function(x) coef(summary(x)))
    Output
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      [1] "No variability observed in a component. Setting batch size to 1"
      $m0a
      $m0a$M1
                       Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
      M12: (Intercept)    0  0    0     0          0     NaN    NaN
      M13: (Intercept)    0  0    0     0          0     NaN    NaN
      M14: (Intercept)    0  0    0     0          0     NaN    NaN
      
      
      $m0b
      $m0b$M2
                       Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
      M22: (Intercept)    0  0    0     0          0     NaN    NaN
      M23: (Intercept)    0  0    0     0          0     NaN    NaN
      M24: (Intercept)    0  0    0     0          0     NaN    NaN
      
      
      $m1a
      $m1a$M1
                       Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
      M12: (Intercept)    0  0    0     0          0     NaN    NaN
      M12: C1             0  0    0     0          0     NaN    NaN
      M13: (Intercept)    0  0    0     0          0     NaN    NaN
      M13: C1             0  0    0     0          0     NaN    NaN
      M14: (Intercept)    0  0    0     0          0     NaN    NaN
      M14: C1             0  0    0     0          0     NaN    NaN
      
      
      $m1b
      $m1b$M2
                       Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
      M22: (Intercept)    0  0    0     0          0     NaN    NaN
      M22: C1             0  0    0     0          0     NaN    NaN
      M23: (Intercept)    0  0    0     0          0     NaN    NaN
      M23: C1             0  0    0     0          0     NaN    NaN
      M24: (Intercept)    0  0    0     0          0     NaN    NaN
      M24: C1             0  0    0     0          0     NaN    NaN
      
      
      $m2a
      $m2a$M1
                       Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
      M12: (Intercept)    0  0    0     0          0     NaN    NaN
      M12: C2             0  0    0     0          0     NaN    NaN
      M13: (Intercept)    0  0    0     0          0     NaN    NaN
      M13: C2             0  0    0     0          0     NaN    NaN
      M14: (Intercept)    0  0    0     0          0     NaN    NaN
      M14: C2             0  0    0     0          0     NaN    NaN
      
      
      $m2b
      $m2b$M2
                       Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
      M22: (Intercept)    0  0    0     0          0     NaN    NaN
      M22: C2             0  0    0     0          0     NaN    NaN
      M23: (Intercept)    0  0    0     0          0     NaN    NaN
      M23: C2             0  0    0     0          0     NaN    NaN
      M24: (Intercept)    0  0    0     0          0     NaN    NaN
      M24: C2             0  0    0     0          0     NaN    NaN
      
      
      $m3a
      $m3a$C1
                  Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
      (Intercept)    0  0    0     0          0     NaN    NaN
      M12            0  0    0     0          0     NaN    NaN
      M13            0  0    0     0          0     NaN    NaN
      M14            0  0    0     0          0     NaN    NaN
      
      
      $m3b
      $m3b$C1
                  Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
      (Intercept)    0  0    0     0          0     NaN    NaN
      M22            0  0    0     0          0     NaN    NaN
      M23            0  0    0     0          0     NaN    NaN
      M24            0  0    0     0          0     NaN    NaN
      
      
      $m4a
      $m4a$M1
                            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
      M12: (Intercept)         0  0    0     0          0     NaN    NaN
      M12: M22                 0  0    0     0          0     NaN    NaN
      M12: M23                 0  0    0     0          0     NaN    NaN
      M12: M24                 0  0    0     0          0     NaN    NaN
      M12: O22                 0  0    0     0          0     NaN    NaN
      M12: O23                 0  0    0     0          0     NaN    NaN
      M12: O24                 0  0    0     0          0     NaN    NaN
      M12: abs(C1 - C2)        0  0    0     0          0     NaN    NaN
      M12: log(C1)             0  0    0     0          0     NaN    NaN
      M12: O22:abs(C1 - C2)    0  0    0     0          0     NaN    NaN
      M12: O23:abs(C1 - C2)    0  0    0     0          0     NaN    NaN
      M12: O24:abs(C1 - C2)    0  0    0     0          0     NaN    NaN
      M13: (Intercept)         0  0    0     0          0     NaN    NaN
      M13: M22                 0  0    0     0          0     NaN    NaN
      M13: M23                 0  0    0     0          0     NaN    NaN
      M13: M24                 0  0    0     0          0     NaN    NaN
      M13: O22                 0  0    0     0          0     NaN    NaN
      M13: O23                 0  0    0     0          0     NaN    NaN
      M13: O24                 0  0    0     0          0     NaN    NaN
      M13: abs(C1 - C2)        0  0    0     0          0     NaN    NaN
      M13: log(C1)             0  0    0     0          0     NaN    NaN
      M13: O22:abs(C1 - C2)    0  0    0     0          0     NaN    NaN
      M13: O23:abs(C1 - C2)    0  0    0     0          0     NaN    NaN
      M13: O24:abs(C1 - C2)    0  0    0     0          0     NaN    NaN
      M14: (Intercept)         0  0    0     0          0     NaN    NaN
      M14: M22                 0  0    0     0          0     NaN    NaN
      M14: M23                 0  0    0     0          0     NaN    NaN
      M14: M24                 0  0    0     0          0     NaN    NaN
      M14: O22                 0  0    0     0          0     NaN    NaN
      M14: O23                 0  0    0     0          0     NaN    NaN
      M14: O24                 0  0    0     0          0     NaN    NaN
      M14: abs(C1 - C2)        0  0    0     0          0     NaN    NaN
      M14: log(C1)             0  0    0     0          0     NaN    NaN
      M14: O22:abs(C1 - C2)    0  0    0     0          0     NaN    NaN
      M14: O23:abs(C1 - C2)    0  0    0     0          0     NaN    NaN
      M14: O24:abs(C1 - C2)    0  0    0     0          0     NaN    NaN
      
      
      $m4b
      $m4b$M1
                                                                      Mean SD 2.5%
      M12: (Intercept)                                                   0  0    0
      M12: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                 0  0    0
      M12: abs(C1 - C2)                                                  0  0    0
      M12: log(C1)                                                       0  0    0
      M12: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)    0  0    0
      M13: (Intercept)                                                   0  0    0
      M13: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                 0  0    0
      M13: abs(C1 - C2)                                                  0  0    0
      M13: log(C1)                                                       0  0    0
      M13: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)    0  0    0
      M14: (Intercept)                                                   0  0    0
      M14: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                 0  0    0
      M14: abs(C1 - C2)                                                  0  0    0
      M14: log(C1)                                                       0  0    0
      M14: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)    0  0    0
                                                                      97.5%
      M12: (Intercept)                                                    0
      M12: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                  0
      M12: abs(C1 - C2)                                                   0
      M12: log(C1)                                                        0
      M12: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)     0
      M13: (Intercept)                                                    0
      M13: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                  0
      M13: abs(C1 - C2)                                                   0
      M13: log(C1)                                                        0
      M13: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)     0
      M14: (Intercept)                                                    0
      M14: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                  0
      M14: abs(C1 - C2)                                                   0
      M14: log(C1)                                                        0
      M14: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)     0
                                                                      tail-prob.
      M12: (Intercept)                                                         0
      M12: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                       0
      M12: abs(C1 - C2)                                                        0
      M12: log(C1)                                                             0
      M12: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)          0
      M13: (Intercept)                                                         0
      M13: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                       0
      M13: abs(C1 - C2)                                                        0
      M13: log(C1)                                                             0
      M13: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)          0
      M14: (Intercept)                                                         0
      M14: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                       0
      M14: abs(C1 - C2)                                                        0
      M14: log(C1)                                                             0
      M14: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)          0
                                                                      GR-crit MCE/SD
      M12: (Intercept)                                                    NaN    NaN
      M12: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                  NaN    NaN
      M12: abs(C1 - C2)                                                   NaN    NaN
      M12: log(C1)                                                        NaN    NaN
      M12: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)     NaN    NaN
      M13: (Intercept)                                                    NaN    NaN
      M13: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                  NaN    NaN
      M13: abs(C1 - C2)                                                   NaN    NaN
      M13: log(C1)                                                        NaN    NaN
      M13: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)     NaN    NaN
      M14: (Intercept)                                                    NaN    NaN
      M14: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0)                  NaN    NaN
      M14: abs(C1 - C2)                                                   NaN    NaN
      M14: log(C1)                                                        NaN    NaN
      M14: ifelse(as.numeric(M2) > as.numeric(O1), 1, 0):abs(C1 - C2)     NaN    NaN
      
      

