Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:22 PM
INPUT INSTRUCTIONS
title: this is an example of a CFA with categorical
factor indicators
montecarlo:
names = u1-u12;
generate = u1-u12(1);
categorical = u1-u12;
nobs = 500;
nreps = 1;
save = ex4.2.dat;
model population:
f1 by u1-u3*.7;
f2 by u4-u6*.7;
f3 by u7-u9*.7;
f4 by u10-u12*.7;
u1-u12*.51;
!V*u*) = 1 so that the parameter metric matches
!that of the Delta parameterization
f1-f4@1;
model:
f1 by u1-u3*.7;
f2 by u4-u6*.7;
f3 by u7-u9*.7;
f4 by u10-u12*.7;
f1-f4@1;
output:
tech9;
INPUT READING TERMINATED NORMALLY
this is an example of a CFA with 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 12
Number of independent variables 0
Number of continuous latent variables 4
Observed dependent variables
Binary and ordered categorical (ordinal)
U1 U2 U3 U4 U5 U6
U7 U8 U9 U10 U11 U12
Continuous latent variables
F1 F2 F3 F4
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 U4$1 U5$1
________ ________ ________ ________ ________
-0.015 -0.040 0.070 0.010 -0.035
Means/Intercepts/Thresholds
U6$1 U7$1 U8$1 U9$1 U10$1
________ ________ ________ ________ ________
0.010 -0.010 -0.020 0.035 -0.010
Means/Intercepts/Thresholds
U11$1 U12$1
________ ________
-0.025 0.005
Covariances/Correlations/Residual Correlations
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
U1
U2 0.593
U3 0.422 0.642
U4 0.019 0.038 0.050
U5 -0.051 -0.096 -0.216 0.552
U6 -0.019 0.026 -0.026 0.426 0.488
U7 0.119 0.025 0.038 -0.113 0.069
U8 0.094 -0.051 -0.024 -0.063 0.018
U9 0.051 0.045 -0.009 -0.019 0.001
U10 -0.144 -0.013 -0.062 -0.050 -0.082
U11 -0.076 0.030 -0.055 -0.069 -0.039
U12 0.063 0.094 0.056 -0.132 -0.150
Covariances/Correlations/Residual Correlations
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
U7 0.038
U8 0.101 0.578
U9 0.131 0.542 0.477
U10 -0.125 0.012 0.012 0.032
U11 -0.119 -0.044 -0.107 -0.087 0.562
U12 -0.082 -0.044 -0.031 0.038 0.409
Covariances/Correlations/Residual Correlations
U11 U12
________ ________
U12 0.547
MODEL FIT INFORMATION
Number of Free Parameters 30
Chi-Square Test of Model Fit
Degrees of freedom 48
Mean 56.595
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 28.177 56.595
0.980 1.000 30.080 56.595
0.950 1.000 33.098 56.595
0.900 1.000 35.949 56.595
0.800 1.000 39.621 56.595
0.700 1.000 42.420 56.595
0.500 1.000 47.335 56.595
0.300 1.000 52.616 56.595
0.200 1.000 55.993 56.595
0.100 0.000 60.907 56.595
0.050 0.000 65.171 56.595
0.020 0.000 70.197 56.595
0.010 0.000 73.683 56.595
RMSEA (Root Mean Square Error Of Approximation)
Mean 0.019
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
CFI/TLI
CFI
Mean 0.990
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 0.987
Std Dev 0.000
Number of successful computations 1
Cumulative Distribution Function
Value Function Value
0.990 1.000
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 0.049
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
U1 0.700 0.6345 0.0000 0.0580 0.0043 1.000 1.000
U2 0.700 0.9296 0.0000 0.0638 0.0527 0.000 1.000
U3 0.700 0.6872 0.0000 0.0588 0.0002 1.000 1.000
F2 BY
U4 0.700 0.6707 0.0000 0.0650 0.0009 1.000 1.000
U5 0.700 0.8114 0.0000 0.0685 0.0124 1.000 1.000
U6 0.700 0.6217 0.0000 0.0633 0.0061 1.000 1.000
F3 BY
U7 0.700 0.8112 0.0000 0.0620 0.0124 1.000 1.000
U8 0.700 0.7119 0.0000 0.0600 0.0001 1.000 1.000
U9 0.700 0.6690 0.0000 0.0593 0.0010 1.000 1.000
F4 BY
U10 0.700 0.6512 0.0000 0.0636 0.0024 1.000 1.000
U11 0.700 0.8502 0.0000 0.0697 0.0226 0.000 1.000
U12 0.700 0.6453 0.0000 0.0630 0.0030 1.000 1.000
F2 WITH
F1 0.000 -0.0673 0.0000 0.0724 0.0045 1.000 0.000
F3 WITH
F1 0.000 0.0519 0.0000 0.0716 0.0027 1.000 0.000
F2 0.000 0.0312 0.0000 0.0750 0.0010 1.000 0.000
F4 WITH
F1 0.000 -0.0140 0.0000 0.0715 0.0002 1.000 0.000
F2 0.000 -0.1776 0.0000 0.0726 0.0315 0.000 1.000
F3 0.000 -0.0559 0.0000 0.0738 0.0031 1.000 0.000
Thresholds
U1$1 0.000 -0.0150 0.0000 0.0561 0.0002 1.000 0.000
U2$1 0.000 -0.0401 0.0000 0.0561 0.0016 1.000 0.000
U3$1 0.000 0.0703 0.0000 0.0561 0.0049 1.000 0.000
U4$1 0.000 0.0100 0.0000 0.0561 0.0001 1.000 0.000
U5$1 0.000 -0.0351 0.0000 0.0561 0.0012 1.000 0.000
U6$1 0.000 0.0100 0.0000 0.0561 0.0001 1.000 0.000
U7$1 0.000 -0.0100 0.0000 0.0561 0.0001 1.000 0.000
U8$1 0.000 -0.0201 0.0000 0.0561 0.0004 1.000 0.000
U9$1 0.000 0.0351 0.0000 0.0561 0.0012 1.000 0.000
U10$1 0.000 -0.0100 0.0000 0.0561 0.0001 1.000 0.000
U11$1 0.000 -0.0251 0.0000 0.0561 0.0006 1.000 0.000
U12$1 0.000 0.0050 0.0000 0.0561 0.0000 1.000 0.000
Variances
F1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
F2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
F3 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
F4 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.118E+00
(ratio of smallest to largest eigenvalue)
TECHNICAL OUTPUT
PARAMETER SPECIFICATION
TAU
U1$1 U2$1 U3$1 U4$1 U5$1
________ ________ ________ ________ ________
1 2 3 4 5
TAU
U6$1 U7$1 U8$1 U9$1 U10$1
________ ________ ________ ________ ________
6 7 8 9 10
TAU
U11$1 U12$1
________ ________
11 12
NU
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0 0 0 0 0
NU
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
0 0 0 0 0
NU
U11 U12
________ ________
0 0
LAMBDA
F1 F2 F3 F4
________ ________ ________ ________
U1 13 0 0 0
U2 14 0 0 0
U3 15 0 0 0
U4 0 16 0 0
U5 0 17 0 0
U6 0 18 0 0
U7 0 0 19 0
U8 0 0 20 0
U9 0 0 21 0
U10 0 0 0 22
U11 0 0 0 23
U12 0 0 0 24
ALPHA
F1 F2 F3 F4
________ ________ ________ ________
0 0 0 0
BETA
F1 F2 F3 F4
________ ________ ________ ________
F1 0 0 0 0
F2 0 0 0 0
F3 0 0 0 0
F4 0 0 0 0
PSI
F1 F2 F3 F4
________ ________ ________ ________
F1 0
F2 25 0
F3 26 27 0
F4 28 29 30 0
STARTING VALUES
TAU
U1$1 U2$1 U3$1 U4$1 U5$1
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
TAU
U6$1 U7$1 U8$1 U9$1 U10$1
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
TAU
U11$1 U12$1
________ ________
0.000 0.000
NU
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
U11 U12
________ ________
0.000 0.000
LAMBDA
F1 F2 F3 F4
________ ________ ________ ________
U1 0.700 0.000 0.000 0.000
U2 0.700 0.000 0.000 0.000
U3 0.700 0.000 0.000 0.000
U4 0.000 0.700 0.000 0.000
U5 0.000 0.700 0.000 0.000
U6 0.000 0.700 0.000 0.000
U7 0.000 0.000 0.700 0.000
U8 0.000 0.000 0.700 0.000
U9 0.000 0.000 0.700 0.000
U10 0.000 0.000 0.000 0.700
U11 0.000 0.000 0.000 0.700
U12 0.000 0.000 0.000 0.700
ALPHA
F1 F2 F3 F4
________ ________ ________ ________
0.000 0.000 0.000 0.000
BETA
F1 F2 F3 F4
________ ________ ________ ________
F1 0.000 0.000 0.000 0.000
F2 0.000 0.000 0.000 0.000
F3 0.000 0.000 0.000 0.000
F4 0.000 0.000 0.000 0.000
PSI
F1 F2 F3 F4
________ ________ ________ ________
F1 1.000
F2 0.000 1.000
F3 0.000 0.000 1.000
F4 0.000 0.000 0.000 1.000
POPULATION VALUES
TAU
U1$1 U2$1 U3$1 U4$1 U5$1
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
TAU
U6$1 U7$1 U8$1 U9$1 U10$1
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
TAU
U11$1 U12$1
________ ________
0.000 0.000
NU
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
U11 U12
________ ________
0.000 0.000
LAMBDA
F1 F2 F3 F4
________ ________ ________ ________
U1 0.700 0.000 0.000 0.000
U2 0.700 0.000 0.000 0.000
U3 0.700 0.000 0.000 0.000
U4 0.000 0.700 0.000 0.000
U5 0.000 0.700 0.000 0.000
U6 0.000 0.700 0.000 0.000
U7 0.000 0.000 0.700 0.000
U8 0.000 0.000 0.700 0.000
U9 0.000 0.000 0.700 0.000
U10 0.000 0.000 0.000 0.700
U11 0.000 0.000 0.000 0.700
U12 0.000 0.000 0.000 0.700
THETA
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
U1 0.510
U2 0.000 0.510
U3 0.000 0.000 0.510
U4 0.000 0.000 0.000 0.510
U5 0.000 0.000 0.000 0.000 0.510
U6 0.000 0.000 0.000 0.000 0.000
U7 0.000 0.000 0.000 0.000 0.000
U8 0.000 0.000 0.000 0.000 0.000
U9 0.000 0.000 0.000 0.000 0.000
U10 0.000 0.000 0.000 0.000 0.000
U11 0.000 0.000 0.000 0.000 0.000
U12 0.000 0.000 0.000 0.000 0.000
THETA
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
U6 0.510
U7 0.000 0.510
U8 0.000 0.000 0.510
U9 0.000 0.000 0.000 0.510
U10 0.000 0.000 0.000 0.000 0.510
U11 0.000 0.000 0.000 0.000 0.000
U12 0.000 0.000 0.000 0.000 0.000
THETA
U11 U12
________ ________
U11 0.510
U12 0.000 0.510
ALPHA
F1 F2 F3 F4
________ ________ ________ ________
0.000 0.000 0.000 0.000
BETA
F1 F2 F3 F4
________ ________ ________ ________
F1 0.000 0.000 0.000 0.000
F2 0.000 0.000 0.000 0.000
F3 0.000 0.000 0.000 0.000
F4 0.000 0.000 0.000 0.000
PSI
F1 F2 F3 F4
________ ________ ________ ________
F1 1.000
F2 0.000 1.000
F3 0.000 0.000 1.000
F4 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
U7
U8
U9
U10
U11
U12
Save file
ex4.2.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:22:39
Ending Time: 22:22:39
Elapsed Time: 00:00:00
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