Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:23 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a CFA with continuous
and categorical factor indicators
montecarlo:
names = u1-u3 y4-y6;
generate = u1-u3(1);
categorical = u1-u3;
nobs = 500;
nreps = 1;
save = ex5.3.dat;
model montecarlo:
f1 by u1@1 u2-u3*1;
f2 by y4@1 y5-y6*1;
u1-y6*.2;
f1-f2*.8;
! note that u* variances should be 1
! in order for the Delta parameterization
! to give estimates in the correct metric
model:
f1 by u1@1 u2-u3*1;
f2 by y4@1 y5-y6*1;
y5-y6*.2;
f1-f2*.8;
output:
tech9;
INPUT READING TERMINATED NORMALLY
this is an example of a CFA with continuous
and categorical factor indicators
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 500
Number of replications
Requested 1
Completed 1
Value of seed 0
Number of dependent variables 6
Number of independent variables 0
Number of continuous latent variables 2
Observed dependent variables
Continuous
Y4 Y5 Y6
Binary and ordered categorical (ordinal)
U1 U2 U3
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
Means/Intercepts/Thresholds
U1$1 U2$1 U3$1 Y4 Y5
________ ________ ________ ________ ________
0.010 0.015 -0.010 0.016 0.016
Means/Intercepts/Thresholds
Y6
________
-0.014
Covariances/Correlations/Residual Correlations
U1 U2 U3 Y4 Y5
________ ________ ________ ________ ________
U1
U2 0.854
U3 0.802 0.855
Y4 0.014 0.000 0.012 1.025
Y5 -0.003 -0.036 -0.029 0.814 1.026
Y6 0.019 -0.016 0.006 0.772 0.811
Covariances/Correlations/Residual Correlations
Y6
________
Y6 0.988
MODEL FIT INFORMATION
Number of Free Parameters 16
Chi-Square Test of Model Fit
Degrees of freedom 8
Mean 3.935
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 1.646 3.935
0.980 1.000 2.032 3.935
0.950 1.000 2.733 3.935
0.900 1.000 3.490 3.935
0.800 0.000 4.594 3.935
0.700 0.000 5.527 3.935
0.500 0.000 7.344 3.935
0.300 0.000 9.524 3.935
0.200 0.000 11.030 3.935
0.100 0.000 13.362 3.935
0.050 0.000 15.507 3.935
0.020 0.000 18.168 3.935
0.010 0.000 20.090 3.935
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 0.010
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
F1 BY
U1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U2 1.000 1.0660 0.0000 0.0432 0.0044 1.000 1.000
U3 1.000 1.0004 0.0000 0.0386 0.0000 1.000 1.000
F2 BY
Y4 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y5 1.000 1.0513 0.0000 0.0393 0.0026 1.000 1.000
Y6 1.000 0.9969 0.0000 0.0410 0.0000 1.000 1.000
F2 WITH
F1 0.000 -0.0041 0.0000 0.0436 0.0000 1.000 0.000
Intercepts
Y4 0.000 -0.0159 0.0000 0.0453 0.0003 1.000 0.000
Y5 0.000 -0.0163 0.0000 0.0454 0.0003 1.000 0.000
Y6 0.000 0.0139 0.0000 0.0445 0.0002 1.000 0.000
Thresholds
U1$1 0.000 0.0100 0.0000 0.0561 0.0001 1.000 0.000
U2$1 0.000 0.0150 0.0000 0.0561 0.0002 1.000 0.000
U3$1 0.000 -0.0100 0.0000 0.0561 0.0001 1.000 0.000
Variances
F1 0.800 0.8014 0.0000 0.0459 0.0000 1.000 1.000
F2 0.800 0.7744 0.0000 0.0619 0.0007 1.000 1.000
Residual Variances
Y4 0.500 0.2507 0.0000 0.0245 0.0622 0.000 1.000
Y5 0.200 0.1700 0.0000 0.0214 0.0009 1.000 1.000
Y6 0.200 0.2184 0.0000 0.0208 0.0003 1.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.393E-02
(ratio of smallest to largest eigenvalue)
TECHNICAL OUTPUT
PARAMETER SPECIFICATION
TAU
U1$1 U2$1 U3$1
________ ________ ________
1 2 3
NU
U1 U2 U3 Y4 Y5
________ ________ ________ ________ ________
0 0 0 4 5
NU
Y6
________
6
LAMBDA
F1 F2
________ ________
U1 0 0
U2 7 0
U3 8 0
Y4 0 0
Y5 0 9
Y6 0 10
THETA
U1 U2 U3 Y4 Y5
________ ________ ________ ________ ________
U1 0
U2 0 0
U3 0 0 0
Y4 0 0 0 11
Y5 0 0 0 0 12
Y6 0 0 0 0 0
THETA
Y6
________
Y6 13
ALPHA
F1 F2
________ ________
0 0
BETA
F1 F2
________ ________
F1 0 0
F2 0 0
PSI
F1 F2
________ ________
F1 14
F2 15 16
STARTING VALUES
TAU
U1$1 U2$1 U3$1
________ ________ ________
0.000 0.000 0.000
NU
U1 U2 U3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
Y6
________
0.000
LAMBDA
F1 F2
________ ________
U1 1.000 0.000
U2 1.066 0.000
U3 1.000 0.000
Y4 0.000 1.000
Y5 0.000 1.051
Y6 0.000 0.997
THETA
U1 U2 U3 Y4 Y5
________ ________ ________ ________ ________
U1 1.000
U2 0.000 1.000
U3 0.000 0.000 1.000
Y4 0.000 0.000 0.000 0.500
Y5 0.000 0.000 0.000 0.000 0.200
Y6 0.000 0.000 0.000 0.000 0.000
THETA
Y6
________
Y6 0.200
ALPHA
F1 F2
________ ________
0.000 0.000
BETA
F1 F2
________ ________
F1 0.000 0.000
F2 0.000 0.000
PSI
F1 F2
________ ________
F1 0.800
F2 0.000 0.800
POPULATION VALUES
TAU
U1$1 U2$1 U3$1
________ ________ ________
0.000 0.000 0.000
NU
U1 U2 U3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
Y6
________
0.000
LAMBDA
F1 F2
________ ________
U1 1.000 0.000
U2 1.000 0.000
U3 1.000 0.000
Y4 0.000 1.000
Y5 0.000 1.000
Y6 0.000 1.000
THETA
U1 U2 U3 Y4 Y5
________ ________ ________ ________ ________
U1 0.200
U2 0.000 0.200
U3 0.000 0.000 0.200
Y4 0.000 0.000 0.000 0.200
Y5 0.000 0.000 0.000 0.000 0.200
Y6 0.000 0.000 0.000 0.000 0.000
THETA
Y6
________
Y6 0.200
ALPHA
F1 F2
________ ________
0.000 0.000
BETA
F1 F2
________ ________
F1 0.000 0.000
F2 0.000 0.000
PSI
F1 F2
________ ________
F1 0.800
F2 0.000 0.800
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
U1
U2
U3
Y4
Y5
Y6
Save file
ex5.3.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:23:11
Ending Time: 22:23:11
Elapsed Time: 00:00:00
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