Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022  10:23 PM

INPUT INSTRUCTIONS

  title:	this is an example of a multiple group CFA
  	with covariates (MIMIC) with categorical
  	factor indicators and a threshold structure

  montecarlo:
  	names = u1-u6 x1-x3;
  	generate = u1-u6(1);
  	categorical = u1-u6;
  	ngroups = 2;
  	nobs = 1000 1200;
  	nreps = 1;
  	save = ex5.16.dat;

  model population:

  	[x1-x3@0]; x1-x3@1;
  	
  	f1 by u1@1 u2-u3*1;
  	f2 by u4@1 u5-u6*1;
  	f1 on x1*.5 x2*.6 x3*.7;
  	f2 on x1*.7 x2*.6 x3*.5;

  	f1-f2*.7;
  	f1 with f2*0;
  	
  	u1-u6*.3;

  	! note that u* variances should be 1
  	! in order for the Delta parameterization
  	! to give estimates in the correct metric

  	[u1$1*-1];
  	[u2$1*-.5];
  	[u3$1*-.25];
  	[u4$1*0];
  	[u5$1*.25];
  	[u6$1*.5];

  	
  model population-g2:

  	f1 by u3*.5;
  	[u3$1*.5];
  	u3*.6; !modified so that u3* variance is 1


  model:


  	f1 by u1@1 u2-u3*1;
  	f2 by u4@1 u5-u6*1;
  	f1 on x1*.5 x2*.6 x3*.7;
  	f2 on x1*.7 x2*.6 x3*.5;

  	f1-f2*.7;
  	f1 with f2*0;

  	[u1$1*-1];
  	[u2$1*-.5];
  	[u3$1*-.25];
  	[u4$1*0];
  	[u5$1*.25];
  	[u6$1*.5];



  	
  model g2:

  	f1 by u3*.5;
  	[u3$1*.5];
  	{u3@1};

  output:
  	tech9;



INPUT READING TERMINATED NORMALLY



this is an example of a multiple group CFA
with covariates (MIMIC) with categorical
factor indicators and a threshold structure

SUMMARY OF ANALYSIS

Number of groups                                                 2
Number of observations
   Group G1                                                   1000
   Group G2                                                   1200
   Total sample size                                          2200

Number of replications
    Requested                                                    1
    Completed                                                    1
Value of seed                                                    0

Number of dependent variables                                    6
Number of independent variables                                  3
Number of continuous latent variables                            2

Observed dependent variables

  Binary and ordered categorical (ordinal)
   U1          U2          U3          U4          U5          U6

Observed independent variables
   X1          X2          X3

Continuous latent variables
   F1          F2


Estimator                                                    WLSMV
Maximum number of iterations                                  1000
Convergence criterion                                    0.500D-04
Maximum number of steepest descent iterations                   20
Parameterization                                             DELTA
Link                                                        PROBIT



SAMPLE STATISTICS FOR THE FIRST REPLICATION


     SAMPLE STATISTICS FOR G1


           Means/Intercepts/Thresholds
              U1$1          U2$1          U3$1          U4$1          U5$1
              ________      ________      ________      ________      ________
               -0.905        -0.536        -0.230        -0.007         0.187


           Means/Intercepts/Thresholds
              U6$1
              ________
                0.504


           Slopes
              X1            X2            X3
              ________      ________      ________
 U1             0.497         0.533         0.638
 U2             0.498         0.560         0.677
 U3             0.474         0.525         0.657
 U4             0.630         0.572         0.493
 U5             0.630         0.637         0.429
 U6             0.670         0.642         0.425


           Covariances/Correlations/Residual Correlations
              U1            U2            U3            U4            U5
              ________      ________      ________      ________      ________
 U1
 U2             0.696
 U3             0.757         0.666
 U4            -0.023        -0.017         0.020
 U5            -0.002        -0.057         0.026         0.713
 U6             0.026        -0.039         0.100         0.674         0.671


           Covariances/Correlations/Residual Correlations
              U6
              ________


     SAMPLE STATISTICS FOR G2


           Means/Intercepts/Thresholds
              U1$1          U2$1          U3$1          U4$1          U5$1
              ________      ________      ________      ________      ________
               -0.990        -0.504         0.563         0.014         0.227


           Means/Intercepts/Thresholds
              U6$1
              ________
                0.484


           Slopes
              X1            X2            X3
              ________      ________      ________
 U1             0.547         0.592         0.756
 U2             0.507         0.672         0.646
 U3             0.308         0.352         0.388
 U4             0.784         0.588         0.532
 U5             0.706         0.592         0.500
 U6             0.680         0.629         0.447


           Covariances/Correlations/Residual Correlations
              U1            U2            U3            U4            U5
              ________      ________      ________      ________      ________
 U1
 U2             0.700
 U3             0.459         0.442
 U4            -0.017        -0.084         0.025
 U5            -0.093        -0.031        -0.034         0.713
 U6            -0.088        -0.053         0.023         0.696         0.727


           Covariances/Correlations/Residual Correlations
              U6
              ________


MODEL FIT INFORMATION

Number of Free Parameters                       37

Chi-Square Test of Model Fit

        Degrees of freedom                      41

        Mean                                33.719
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       1.000           22.906         33.719
           0.980       1.000           24.609         33.719
           0.950       1.000           27.326         33.719
           0.900       1.000           29.907         33.719
           0.800       1.000           33.251         33.719
           0.700       0.000           35.813         33.719
           0.500       0.000           40.335         33.719
           0.300       0.000           45.224         33.719
           0.200       0.000           48.363         33.719
           0.100       0.000           52.949         33.719
           0.050       0.000           56.942         33.719
           0.020       0.000           61.665         33.719
           0.010       0.000           64.950         33.719

RMSEA (Root Mean Square Error Of Approximation)

        Mean                                 0.000
        Std Dev                              0.000
        Number of successful computations        1

        Cumulative Distribution Function
           Value    Function Value
           0.990       1.000
           0.980       1.000
           0.950       1.000
           0.900       1.000
           0.800       1.000
           0.700       1.000
           0.500       1.000
           0.300       1.000
           0.200       1.000
           0.100       1.000
           0.050       1.000
           0.020       1.000
           0.010       1.000

CFI/TLI

    CFI

        Mean                                 1.000
        Std Dev                              0.000
        Number of successful computations        1

        Cumulative Distribution Function
           Value    Function Value
           0.990       0.000
           0.980       0.000
           0.950       0.000
           0.900       0.000
           0.800       0.000
           0.700       0.000
           0.500       0.000
           0.300       0.000
           0.200       0.000
           0.100       0.000
           0.050       0.000
           0.020       0.000
           0.010       0.000

    TLI

        Mean                                 1.000
        Std Dev                              0.000
        Number of successful computations        1

        Cumulative Distribution Function
           Value    Function Value
           0.990       0.000
           0.980       0.000
           0.950       0.000
           0.900       0.000
           0.800       0.000
           0.700       0.000
           0.500       0.000
           0.300       0.000
           0.200       0.000
           0.100       0.000
           0.050       0.000
           0.020       0.000
           0.010       0.000

SRMR (Standardized Root Mean Square Residual)

        Mean                                 0.016
        Std Dev                              0.000
        Number of successful computations        1

        Cumulative Distribution Function
           Value    Function Value
           0.990       1.000
           0.980       1.000
           0.950       1.000
           0.900       1.000
           0.800       1.000
           0.700       1.000
           0.500       1.000
           0.300       1.000
           0.200       1.000
           0.100       1.000
           0.050       1.000
           0.020       1.000
           0.010       0.000


MODEL RESULTS

                              ESTIMATES              S. E.     M. S. E.  95%  % Sig
                 Population   Average   Std. Dev.   Average             Cover Coeff

Group G1

 F1       BY
  U1                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  U2                  1.000     0.9574     0.0000     0.0488     0.0018 1.000 1.000
  U3                  1.000     0.9777     0.0000     0.0487     0.0005 1.000 1.000

 F2       BY
  U4                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  U5                  1.000     1.0017     0.0000     0.0438     0.0000 1.000 1.000
  U6                  1.000     0.9916     0.0000     0.0450     0.0001 1.000 1.000

 F1       ON
  X1                  0.500     0.4995     0.0000     0.0442     0.0000 1.000 1.000
  X2                  0.600     0.5505     0.0000     0.0447     0.0025 1.000 1.000
  X3                  0.700     0.6708     0.0000     0.0463     0.0009 1.000 1.000

 F2       ON
  X1                  0.700     0.6438     0.0000     0.0451     0.0032 1.000 1.000
  X2                  0.600     0.6188     0.0000     0.0434     0.0004 1.000 1.000
  X3                  0.500     0.4501     0.0000     0.0413     0.0025 1.000 1.000

 F1       WITH
  F2                  0.000     0.0050     0.0000     0.0430     0.0000 1.000 0.000

 Intercepts
  F1                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  F2                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

 Thresholds
  U1$1               -1.000    -0.9052     0.0000     0.0568     0.0090 1.000 1.000
  U2$1               -0.500    -0.5358     0.0000     0.0517     0.0013 1.000 1.000
  U3$1               -0.250    -0.2297     0.0000     0.0467     0.0004 1.000 1.000
  U4$1                0.000    -0.0134     0.0000     0.0452     0.0002 1.000 0.000
  U5$1                0.250     0.1982     0.0000     0.0424     0.0027 1.000 1.000
  U6$1                0.500     0.4989     0.0000     0.0485     0.0000 1.000 1.000

 Residual Variances
  F1                  0.700     0.7406     0.0000     0.0508     0.0017 1.000 1.000
  F2                  0.700     0.6911     0.0000     0.0444     0.0001 1.000 1.000

 Scales
  U1                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  U2                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  U3                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  U4                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  U5                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  U6                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000

Group G2

 F1       BY
  U1                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  U2                  1.000     0.9574     0.0000     0.0488     0.0018 1.000 1.000
  U3                  0.500     0.7754     0.0000     0.1657     0.0758 1.000 1.000

 F2       BY
  U4                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  U5                  1.000     1.0017     0.0000     0.0438     0.0000 1.000 1.000
  U6                  1.000     0.9916     0.0000     0.0450     0.0001 1.000 1.000

 F1       ON
  X1                  0.500     0.3979     0.0000     0.0862     0.0104 1.000 1.000
  X2                  0.600     0.4719     0.0000     0.1004     0.0164 1.000 1.000
  X3                  0.700     0.5224     0.0000     0.1106     0.0315 1.000 1.000

 F2       ON
  X1                  0.700     0.7799     0.0000     0.1210     0.0064 1.000 1.000
  X2                  0.600     0.6476     0.0000     0.1032     0.0023 1.000 1.000
  X3                  0.500     0.5302     0.0000     0.0875     0.0009 1.000 1.000

 F1       WITH
  F2                  0.000    -0.0392     0.0000     0.0364     0.0015 1.000 0.000

 Intercepts
  F1                  0.000    -0.1704     0.0000     0.1280     0.0290 1.000 0.000
  F2                  0.000    -0.0347     0.0000     0.0636     0.0012 1.000 0.000

 Thresholds
  U1$1               -1.000    -0.9052     0.0000     0.0568     0.0090 1.000 1.000
  U2$1               -0.500    -0.5358     0.0000     0.0517     0.0013 1.000 1.000
  U3$1                0.500     0.4311     0.0000     0.1290     0.0047 1.000 1.000
  U4$1                0.000    -0.0134     0.0000     0.0452     0.0002 1.000 0.000
  U5$1                0.250     0.1982     0.0000     0.0424     0.0027 1.000 1.000
  U6$1                0.500     0.4989     0.0000     0.0485     0.0000 1.000 1.000

 Residual Variances
  F1                  0.700     0.4111     0.0000     0.1724     0.0835 1.000 1.000
  F2                  0.700     0.8295     0.0000     0.2509     0.0168 1.000 1.000

 Scales
  U1                  1.000     1.3465     0.0000     0.2748     0.1200 1.000 1.000
  U2                  1.000     1.3528     0.0000     0.3017     0.1245 1.000 1.000
  U3                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  U4                  1.000     0.9391     0.0000     0.1415     0.0037 1.000 1.000
  U5                  1.000     0.9314     0.0000     0.1416     0.0047 1.000 1.000
  U6                  1.000     0.9170     0.0000     0.1334     0.0069 1.000 1.000


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.256E-03
       (ratio of smallest to largest eigenvalue)


TECHNICAL OUTPUT


     PARAMETER SPECIFICATION FOR G1


           TAU
              U1$1          U2$1          U3$1          U4$1          U5$1
              ________      ________      ________      ________      ________
                  1             2             3             4             5


           TAU
              U6$1
              ________
                  6


           NU
              U1            U2            U3            U4            U5
              ________      ________      ________      ________      ________
                  0             0             0             0             0


           NU
              U6
              ________
                  0


           LAMBDA
              F1            F2
              ________      ________
 U1                 0             0
 U2                 7             0
 U3                 8             0
 U4                 0             0
 U5                 0             9
 U6                 0            10


           ALPHA
              F1            F2
              ________      ________
                  0             0


           BETA
              F1            F2
              ________      ________
 F1                 0             0
 F2                 0             0


           GAMMA
              X1            X2            X3
              ________      ________      ________
 F1                11            12            13
 F2                14            15            16


           PSI
              F1            F2
              ________      ________
 F1                17
 F2                18            19


           DELTA
              U1            U2            U3            U4            U5
              ________      ________      ________      ________      ________
                  0             0             0             0             0


           DELTA
              U6
              ________
                  0


     PARAMETER SPECIFICATION FOR G2


           TAU
              U1$1          U2$1          U3$1          U4$1          U5$1
              ________      ________      ________      ________      ________
                  1             2            20             4             5


           TAU
              U6$1
              ________
                  6


           NU
              U1            U2            U3            U4            U5
              ________      ________      ________      ________      ________
                  0             0             0             0             0


           NU
              U6
              ________
                  0


           LAMBDA
              F1            F2
              ________      ________
 U1                 0             0
 U2                 7             0
 U3                21             0
 U4                 0             0
 U5                 0             9
 U6                 0            10


           ALPHA
              F1            F2
              ________      ________
                 22            23


           BETA
              F1            F2
              ________      ________
 F1                 0             0
 F2                 0             0


           GAMMA
              X1            X2            X3
              ________      ________      ________
 F1                24            25            26
 F2                27            28            29


           PSI
              F1            F2
              ________      ________
 F1                30
 F2                31            32


           DELTA
              U1            U2            U3            U4            U5
              ________      ________      ________      ________      ________
                 33            34             0            35            36


           DELTA
              U6
              ________
                 37


     STARTING VALUES FOR G1


           TAU
              U1$1          U2$1          U3$1          U4$1          U5$1
              ________      ________      ________      ________      ________
               -1.000        -0.500        -0.250         0.000         0.250


           TAU
              U6$1
              ________
                0.500


           NU
              U1            U2            U3            U4            U5
              ________      ________      ________      ________      ________
                0.000         0.000         0.000         0.000         0.000


           NU
              U6
              ________
                0.000


           LAMBDA
              F1            F2
              ________      ________
 U1             1.000         0.000
 U2             0.879         0.000
 U3             0.957         0.000
 U4             0.000         1.000
 U5             0.000         0.995
 U6             0.000         0.940


           ALPHA
              F1            F2
              ________      ________
                0.000         0.000


           BETA
              F1            F2
              ________      ________
 F1             0.000         0.000
 F2             0.000         0.000


           GAMMA
              X1            X2            X3
              ________      ________      ________
 F1             0.500         0.600         0.700
 F2             0.700         0.600         0.500


           PSI
              F1            F2
              ________      ________
 F1             0.700
 F2             0.000         0.700


           DELTA
              U1            U2            U3            U4            U5
              ________      ________      ________      ________      ________
                1.000         1.000         1.000         1.000         1.000


           DELTA
              U6
              ________
                1.000


     STARTING VALUES FOR G2


           TAU
              U1$1          U2$1          U3$1          U4$1          U5$1
              ________      ________      ________      ________      ________
               -1.000        -0.500         0.500         0.000         0.250


           TAU
              U6$1
              ________
                0.500


           NU
              U1            U2            U3            U4            U5
              ________      ________      ________      ________      ________
                0.000         0.000         0.000         0.000         0.000


           NU
              U6
              ________
                0.000


           LAMBDA
              F1            F2
              ________      ________
 U1             1.000         0.000
 U2             1.000         0.000
 U3             0.500         0.000
 U4             0.000         1.000
 U5             0.000         1.044
 U6             0.000         1.019


           ALPHA
              F1            F2
              ________      ________
                0.000         0.000


           BETA
              F1            F2
              ________      ________
 F1             0.000         0.000
 F2             0.000         0.000


           GAMMA
              X1            X2            X3
              ________      ________      ________
 F1             0.500         0.600         0.700
 F2             0.700         0.600         0.500


           PSI
              F1            F2
              ________      ________
 F1             0.700
 F2             0.000         0.700


           DELTA
              U1            U2            U3            U4            U5
              ________      ________      ________      ________      ________
                1.000         1.000         1.000         1.000         1.000


           DELTA
              U6
              ________
                1.000


     POPULATION VALUES FOR G1


           TAU
              U1$1          U2$1          U3$1          U4$1          U5$1
              ________      ________      ________      ________      ________
               -1.000        -0.500        -0.250         0.000         0.250


           TAU
              U6$1
              ________
                0.500


           NU
              U1            U2            U3            U4            U5
              ________      ________      ________      ________      ________
                0.000         0.000         0.000         0.000         0.000


           NU
              U6            X1            X2            X3
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           LAMBDA
              F1            F2            X1            X2            X3
              ________      ________      ________      ________      ________
 U1             1.000         0.000         0.000         0.000         0.000
 U2             1.000         0.000         0.000         0.000         0.000
 U3             1.000         0.000         0.000         0.000         0.000
 U4             0.000         1.000         0.000         0.000         0.000
 U5             0.000         1.000         0.000         0.000         0.000
 U6             0.000         1.000         0.000         0.000         0.000
 X1             0.000         0.000         1.000         0.000         0.000
 X2             0.000         0.000         0.000         1.000         0.000
 X3             0.000         0.000         0.000         0.000         1.000


           THETA
              U1            U2            U3            U4            U5
              ________      ________      ________      ________      ________
 U1             0.300
 U2             0.000         0.300
 U3             0.000         0.000         0.300
 U4             0.000         0.000         0.000         0.300
 U5             0.000         0.000         0.000         0.000         0.300
 U6             0.000         0.000         0.000         0.000         0.000
 X1             0.000         0.000         0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000         0.000
 X3             0.000         0.000         0.000         0.000         0.000


           THETA
              U6            X1            X2            X3
              ________      ________      ________      ________
 U6             0.300
 X1             0.000         0.000
 X2             0.000         0.000         0.000
 X3             0.000         0.000         0.000         0.000


           ALPHA
              F1            F2            X1            X2            X3
              ________      ________      ________      ________      ________
                0.000         0.000         0.000         0.000         0.000


           BETA
              F1            F2            X1            X2            X3
              ________      ________      ________      ________      ________
 F1             0.000         0.000         0.500         0.600         0.700
 F2             0.000         0.000         0.700         0.600         0.500
 X1             0.000         0.000         0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000         0.000
 X3             0.000         0.000         0.000         0.000         0.000


           PSI
              F1            F2            X1            X2            X3
              ________      ________      ________      ________      ________
 F1             0.700
 F2             0.000         0.700
 X1             0.000         0.000         1.000
 X2             0.000         0.000         0.000         1.000
 X3             0.000         0.000         0.000         0.000         1.000


     POPULATION VALUES FOR G2


           TAU
              U1$1          U2$1          U3$1          U4$1          U5$1
              ________      ________      ________      ________      ________
               -1.000        -0.500         0.500         0.000         0.250


           TAU
              U6$1
              ________
                0.500


           NU
              U1            U2            U3            U4            U5
              ________      ________      ________      ________      ________
                0.000         0.000         0.000         0.000         0.000


           NU
              U6            X1            X2            X3
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           LAMBDA
              F1            F2            X1            X2            X3
              ________      ________      ________      ________      ________
 U1             1.000         0.000         0.000         0.000         0.000
 U2             1.000         0.000         0.000         0.000         0.000
 U3             0.500         0.000         0.000         0.000         0.000
 U4             0.000         1.000         0.000         0.000         0.000
 U5             0.000         1.000         0.000         0.000         0.000
 U6             0.000         1.000         0.000         0.000         0.000
 X1             0.000         0.000         1.000         0.000         0.000
 X2             0.000         0.000         0.000         1.000         0.000
 X3             0.000         0.000         0.000         0.000         1.000


           THETA
              U1            U2            U3            U4            U5
              ________      ________      ________      ________      ________
 U1             0.300
 U2             0.000         0.300
 U3             0.000         0.000         0.600
 U4             0.000         0.000         0.000         0.300
 U5             0.000         0.000         0.000         0.000         0.300
 U6             0.000         0.000         0.000         0.000         0.000
 X1             0.000         0.000         0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000         0.000
 X3             0.000         0.000         0.000         0.000         0.000


           THETA
              U6            X1            X2            X3
              ________      ________      ________      ________
 U6             0.300
 X1             0.000         0.000
 X2             0.000         0.000         0.000
 X3             0.000         0.000         0.000         0.000


           ALPHA
              F1            F2            X1            X2            X3
              ________      ________      ________      ________      ________
                0.000         0.000         0.000         0.000         0.000


           BETA
              F1            F2            X1            X2            X3
              ________      ________      ________      ________      ________
 F1             0.000         0.000         0.500         0.600         0.700
 F2             0.000         0.000         0.700         0.600         0.500
 X1             0.000         0.000         0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000         0.000
 X3             0.000         0.000         0.000         0.000         0.000


           PSI
              F1            F2            X1            X2            X3
              ________      ________      ________      ________      ________
 F1             0.700
 F2             0.000         0.700
 X1             0.000         0.000         1.000
 X2             0.000         0.000         0.000         1.000
 X3             0.000         0.000         0.000         0.000         1.000


TECHNICAL 9 OUTPUT

  Error messages for each replication (if any)



SAVEDATA INFORMATION

  Order of variables

    U1
    U2
    U3
    U4
    U5
    U6
    X1
    X2
    X3
    GROUP

  Save file
    ex5.16.dat

  Save file format           Free
  Save file record length    10000


     Beginning Time:  22:23:02
        Ending Time:  22:23:03
       Elapsed Time:  00:00:01



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