```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

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

MUTHEN & MUTHEN
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Los Angeles, CA  90066

Tel: (310) 391-9971
Fax: (310) 391-8971
Web: www.StatModel.com
Support: Support@StatModel.com

Copyright (c) 1998-2022 Muthen & Muthen
```