```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;

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

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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