Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:22 PM
INPUT INSTRUCTIONS
title: this is an example of a threshold
structure CFA for categorical factor indicators
montecarlo:
names = u1a u1b u1c u2a u2b u2c;
generate = u1a-u2c(1);
categorical = u1a-u2c;
nobs = 500;
nreps = 1;
save = ex5.10.dat;
model population:
f1 by u1a-u1c@1;
f2 by u2a-u2c@1;
[u1a$1*-.5 u1b$1*-.5 u1c$1*-.5] (1);
[u2a$1*.5 u2b$1*.5 u2c$1*.5] (2);
u1a-u2c*.5;
f1-f2*.5; f1 with f2*.2;
! note that u* variances should be 1
! in order for the Delta parameterization
! to give estimates in the correct metric
model:
f1 by u1a-u1c@1;
f2 by u2a-u2c@1;
[u1a$1*-.5 u1b$1*-.5 u1c$1*-.5] (1);
[u2a$1*.5 u2b$1*.5 u2c$1*.5] (2);
f1-f2*.5; f1 with f2*.2;
INPUT READING TERMINATED NORMALLY
this is an example of a threshold
structure CFA for 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
Binary and ordered categorical (ordinal)
U1A U1B U1C U2A U2B U2C
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
U1A$1 U1B$1 U1C$1 U2A$1 U2B$1
________ ________ ________ ________ ________
-0.479 -0.577 -0.490 0.577 0.536
Means/Intercepts/Thresholds
U2C$1
________
0.507
Covariances/Correlations/Residual Correlations
U1A U1B U1C U2A U2B
________ ________ ________ ________ ________
U1A
U1B 0.504
U1C 0.464 0.513
U2A 0.215 0.085 0.154
U2B 0.196 0.082 0.204 0.470
U2C 0.303 0.211 0.110 0.514 0.579
Covariances/Correlations/Residual Correlations
U2C
________
MODEL FIT INFORMATION
Number of Free Parameters 5
Chi-Square Test of Model Fit
Degrees of freedom 16
Mean 15.119
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 5.812 15.119
0.980 1.000 6.614 15.119
0.950 1.000 7.962 15.119
0.900 1.000 9.312 15.119
0.800 1.000 11.152 15.119
0.700 1.000 12.624 15.119
0.500 0.000 15.338 15.119
0.300 0.000 18.418 15.119
0.200 0.000 20.465 15.119
0.100 0.000 23.542 15.119
0.050 0.000 26.296 15.119
0.020 0.000 29.633 15.119
0.010 0.000 32.000 15.119
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 0.044
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 0.000
0.010 0.000
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
F1 BY
U1A 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U1B 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U1C 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
F2 BY
U2A 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U2B 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U2C 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
F1 WITH
F2 0.200 0.1760 0.0000 0.0400 0.0006 1.000 1.000
Thresholds
U1A$1 -0.500 -0.5146 0.0000 0.0433 0.0002 1.000 1.000
U1B$1 -0.500 -0.5146 0.0000 0.0433 0.0002 1.000 1.000
U1C$1 -0.500 -0.5146 0.0000 0.0433 0.0002 1.000 1.000
U2A$1 0.500 0.5397 0.0000 0.0441 0.0016 1.000 1.000
U2B$1 0.500 0.5397 0.0000 0.0441 0.0016 1.000 1.000
U2C$1 0.500 0.5397 0.0000 0.0441 0.0016 1.000 1.000
Variances
F1 0.500 0.4940 0.0000 0.0431 0.0000 1.000 1.000
F2 0.500 0.5257 0.0000 0.0435 0.0007 1.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.504E+00
(ratio of smallest to largest eigenvalue)
TECHNICAL OUTPUT
PARAMETER SPECIFICATION
TAU
U1A$1 U1B$1 U1C$1 U2A$1 U2B$1
________ ________ ________ ________ ________
1 1 1 2 2
TAU
U2C$1
________
2
NU
U1A U1B U1C U2A U2B
________ ________ ________ ________ ________
0 0 0 0 0
NU
U2C
________
0
LAMBDA
F1 F2
________ ________
U1A 0 0
U1B 0 0
U1C 0 0
U2A 0 0
U2B 0 0
U2C 0 0
ALPHA
F1 F2
________ ________
0 0
BETA
F1 F2
________ ________
F1 0 0
F2 0 0
PSI
F1 F2
________ ________
F1 3
F2 4 5
STARTING VALUES
TAU
U1A$1 U1B$1 U1C$1 U2A$1 U2B$1
________ ________ ________ ________ ________
-0.500 -0.500 -0.500 0.500 0.500
TAU
U2C$1
________
0.500
NU
U1A U1B U1C U2A U2B
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
U2C
________
0.000
LAMBDA
F1 F2
________ ________
U1A 1.000 0.000
U1B 1.000 0.000
U1C 1.000 0.000
U2A 0.000 1.000
U2B 0.000 1.000
U2C 0.000 1.000
ALPHA
F1 F2
________ ________
0.000 0.000
BETA
F1 F2
________ ________
F1 0.000 0.000
F2 0.000 0.000
PSI
F1 F2
________ ________
F1 0.500
F2 0.200 0.500
POPULATION VALUES
TAU
U1A$1 U1B$1 U1C$1 U2A$1 U2B$1
________ ________ ________ ________ ________
-0.500 -0.500 -0.500 0.500 0.500
TAU
U2C$1
________
0.500
NU
U1A U1B U1C U2A U2B
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
U2C
________
0.000
LAMBDA
F1 F2
________ ________
U1A 1.000 0.000
U1B 1.000 0.000
U1C 1.000 0.000
U2A 0.000 1.000
U2B 0.000 1.000
U2C 0.000 1.000
THETA
U1A U1B U1C U2A U2B
________ ________ ________ ________ ________
U1A 0.500
U1B 0.000 0.500
U1C 0.000 0.000 0.500
U2A 0.000 0.000 0.000 0.500
U2B 0.000 0.000 0.000 0.000 0.500
U2C 0.000 0.000 0.000 0.000 0.000
THETA
U2C
________
U2C 0.500
ALPHA
F1 F2
________ ________
0.000 0.000
BETA
F1 F2
________ ________
F1 0.000 0.000
F2 0.000 0.000
PSI
F1 F2
________ ________
F1 0.500
F2 0.200 0.500
SAVEDATA INFORMATION
Order of variables
U1A
U1B
U1C
U2A
U2B
U2C
Save file
ex5.10.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:22:57
Ending Time: 22:22:57
Elapsed Time: 00:00:00
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