TITLE: CSC(M-1) change model
         with multiple groups and ordinal indicators.
         There are 2 constructs each measured by 6 items from 2 raters
         - PROSOCIAL BEHAVIOR (PB)
         - RELATIONAL AGGRESSION (RA)
         All lines beginning with an exclamation mark represent comments
         Least restrictive model (1) with the following restrictions
         a) residual variances = 1 in first group
         b) factor means = 0 in first group
         c) one loading per factor = 1 in each group
         d) two thresholds per indicator invariant across groups


  ! Definition of the ASCII data file to be used
  DATA: FILE = Papilio.dat;

  ! Naming of the variables in the file
  VARIABLE: NAMES = treat group
                    tPB13 tPB12 tPB11
                    pPB13 pPB12 pPB11
                    tPB23 tPB22 tPB21
                    pPB23 pPB22 pPB21
                    tRA11 tRA12 tRA13
                    pRA11 pRA12 pRA13
                    tRA21 tRA22 tRA23
                    pRA21 pRA22 pRA23;

  ! Observed variables (items) to be used in the analysis
  ! Yijkl: i = indicator, j = construct, k = method, l = time point
            USEVARIABLES =
            ! Prosocial Behavior teacher ratings (time point 1)
            ! represent Y1111, Y2111, and Y3111
              tPB11 tPB12 tPB13
            ! Prosocial Behavior parent ratings (time point 1)
            ! represent Y1121, Y2121, and Y3121
              pPB11 pPB12 pPB13
            ! Prosocial Behavior teacher ratings (time point 2)
            ! represent Y1112, Y2112, and Y3112
              tPB21 tPB22 tPB23
            ! Prosocial Behavior parent ratings (time point 2)
            ! represent Y1122, Y2122, and Y3122
              pPB21 pPB22 pPB23
            ! Relational Aggression teacher ratings (time point 1)
            ! represent Y1211, Y2211, and Y3211
              tRA11 tRA12 tRA13
            ! Relational Aggression parent ratings (time point 1)
            ! represent Y1221, Y2221, and Y3221
              pRA11 pRA12 pRA13
            ! Relational Aggression teacher ratings (time point 2)
            ! represent Y1212, Y2212, and Y3212
              tRA21 tRA22 tRA23
            ! Relational Aggression parent ratings (time point 2)
            ! represent Y1222, Y2222, and Y3222
              pRA21 pRA22 pRA23;

  ! Definition of observed variables as ordinal
            CATEGORICAL =
              tPB11 tPB12 tPB13
              pPB11 pPB12 pPB13
              tPB21 tPB22 tPB23
              pPB21 pPB22 pPB23
              tRA11 tRA12 tRA13
              pRA11 pRA12 pRA13
              tRA21 tRA22 tRA23
              pRA21 pRA22 pRA23;

  ! Missing value flag
  ! All missing values are coded -9
            MISSING = all(-9);

  ! Definition of the cluster variable
  ! Children where nested within groups
            CLUSTER = group;

  ! Definition of the grouping variable
  ! This indicates control group (CG) and intervention group (IG)
            GROUPING = treat (0 = CG 1 = IG);

  ! This type of analysis takes clustering of observations into account
  ANALYSIS: TYPE = COMPLEX;
            ! The WLSMV is the default estimator for this analysis
            ! when at least one dependent categorical variable is involved
            ESTIMATOR = WLSMV;
            ! Change the default Delta parameterization to Theta
            PARAMETERIZATION = THETA;

  ! Model specification
  MODEL:
         ! The first method k = 1 is selected as reference method
         ! Definiton of a Prosocial Behavior factor PB1 at time point 1
         PB1 by tPB11
                tPB12
                tPB13
                pPB11
                pPB12
                pPB13;

         ! Definiton of a Prosocial Behavior factor PB2 at time point 2
         PB2 by tPB21
                tPB22
                tPB23
                pPB21
                pPB22
                pPB23;

         ! Definition of a Relational Aggression factor RA1 at time point 1
         RA1 by tRA11
                tRA12
                tRA13
                pRA11
                pRA12
                pRA13;

         ! Definition of a Relational Aggression factor RA2 at time point 2
         RA2 by tRA21
                tRA22
                tRA23
                pRA21
                pRA22
                pRA23;

         ! For indicators belonging to the non-reference method k = 2
         ! a construct-specific method factor is defined
         ! Prosocial Behavior Method factor MPB1 time point 1
         MPB1 by pPB11
                 pPB12
                 pPB13;

         ! Prosocial Behavior Method factor MPB2 time point 2
         MPB2 by pPB21
                 pPB22
                 pPB23;

         ! Relational Aggression Method factor MRA1 time point 1
         MRA1 by pRA11
                 pRA12
                 pRA13;

         ! Relational Aggression Method factor MRA2 time point 2
         MRA2 by pRA21
                 pRA22
                 pRA23;

         ! Item-specific factors 
         !Item 3 PB teacher
         tPB3 by tPB13
                 tPB23;
        ! Item 3 PB parent
         pPB3 by pPB13
                 pPB23;
        ! Item 2 RA parent
         pRA2 by pRA12
                 pRA22;
        ! Item 3 RA parent
         pRA3 by pRA13
                 pRA23;   

       ! Definition of change factor PBC
       PBC by;
       PB2 on PB1@1 PBC@1;
       PB2@0;
       [PB2@0];
       
       ! Definition of change factor RAC
       RAC by;
       RA2 on RA1@1 RAC@1;
       RA2@0;
       [RA2@0];

       ! Definition of change factor MPBC
       MPBC by;
       MPB2 on MPB1@1 MPBC@1;
       MPB2@0;
       [MPB2@0];

       ! Definition of change factor MRAC
       MRAC by;
       MRA2 on MRA1@1 MRAC@1;
       MRA2@0;
       [MRA2@0];

      ! Restrictions in the structural model
      PB1 with MPB1@0 MPB2@0 MPBC@0 RA2@0 MRA2@0 tPB3@0 pPB3@0;
      PBC with MPB1@0 MPB2@0 MPBC@0 RA2@0 MRA2@0 tPB3@0 pPB3@0;
      PB2 with MPB1@0 MPB2@0 MPBC@0 tPB3@0 pPB3@0 pRA2@0 pRA3@0
               MRA1@0 MRA2@0 MRAC@0 RA1@0 RA2@0 RAC@0;

      RA1 with MRA1@0 MRA2@0 MRAC@0 MPB2@0 pRA2@0 pRA3@0;
      RAC with MRA1@0 MRA2@0 MRAC@0 MPB2@0 pRA2@0 pRA3@0;      
      RA2 with MPB1@0 MPB2@0 MPBC@0 pRA2@0 pRA3@0 tPB3@0 pPB3@0
               MRA1@0 MRA2@0 MRAC@0;

      MPB1 with MRA2@0 pPB3@0;
      MPBC with MRA2@0 pPB3@0;
      MPB2 with MRA1@0 MRA2@0 MRAC@0 pRA2@0 pRA3@0 tPB3@0 pPB3@0;

      MRA1 with pRA2@0 pRA3@0;
      MRAC with pRA2@0 pRA3@0;
      MRA2 with pRA2@0 pRA3@0 tPB3@0 pPB3@0;

         ! Fix means of residual factors to 0
         [MPB1@0 MPBC@0 tPB3@0 pPB3@0];
         [MRA1@0 MRAC@0 pRA2@0 pRA3@0];

  ! In the control (reference) group
  MODEL CG:
         ! Fix latent factor means to 0
         [PB1@0 PBC@0 RA1@0 RAC@0];
         ! Fix residual variances to 1
         tPB11-pRA23@1;

  ! In the intervention group
  ! Repeat BY statements to allow loading parameters to differ
  MODEL IG:
                 ! The first method k = 1 is selected as reference method
         ! Definiton of a Prosocial Behavior factor PB1 at time point 1
         PB1 by tPB11@1
                tPB12
                tPB13
                pPB11
                pPB12
                pPB13;

         ! Definiton of a Prosocial Behavior factor PB2 at time point 2
         PB2 by tPB21@1
                tPB22
                tPB23
                pPB21
                pPB22
                pPB23;

         ! Definition of a Relational Aggression factor RA1 at time point 1
         RA1 by tRA11@1
                tRA12
                tRA13
                pRA11
                pRA12
                pRA13;

         ! Definition of a Relational Aggression factor RA2 at time point 2
         RA2 by tRA21@1
                tRA22
                tRA23
                pRA21
                pRA22
                pRA23;

         ! For indicators belonging to the non-reference method k = 2
         ! a construct-specific method factor is defined
         ! Prosocial Behavior Method factor MPB1 time point 1
         MPB1 by pPB11@1
                 pPB12
                 pPB13;

         ! Prosocial Behavior Method factor MPB2 time point 2
         MPB2 by pPB21@1
                 pPB22
                 pPB23;

         ! Relational Aggression Method factor MRA1 time point 1
         MRA1 by pRA11@1
                 pRA12
                 pRA13;

         ! Relational Aggression Method factor MRA2 time point 2
         MRA2 by pRA21@1
                 pRA22
                 pRA23;

                          ! Item-specific factors 
         !Item 3 PB teacher
         tPB3 by tPB13@1
                 tPB23;
        ! Item 3 PB parent
         pPB3 by pPB13@1
                 pPB23;
        ! Item 2 RA parent
         pRA2 by pRA12@1
                 pRA22;
        ! Item 3 RA parent
         pRA3 by pRA13@1
                 pRA23;   

  OUTPUT: SAMPSTAT STDYX TECH1 TECH4;
  SAVEDATA: DIFFTEST = 1_minimal_neu.dat;