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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