```Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022  10:23 PM

INPUT INSTRUCTIONS

TITLE:	this is an example of a CFA with categorical factor indicators

montecarlo:
names = u1-u6;
generate = u1-u6(1);
categorical = u1-u6;
nobs = 500;
nreps = 1;
save = ex5.2.dat;

model montecarlo:

f1 by u1@1 u2-u3*1;
f2 by u4@1 u5-u6*1;
u1-u6*.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 u4@1 u5-u6*1;

f1-f2*.8;

output:
tech9;

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                                    6
Number of independent variables                                  0
Number of continuous latent variables                            2

Observed dependent variables

Binary and ordered categorical (ordinal)
U1          U2          U3          U4          U5          U6

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

SAMPLE STATISTICS FOR THE FIRST REPLICATION

SAMPLE STATISTICS

Means/Intercepts/Thresholds
U1\$1          U2\$1          U3\$1          U4\$1          U5\$1
________      ________      ________      ________      ________
0.010         0.015        -0.010         0.060         0.020

Means/Intercepts/Thresholds
U6\$1
________
0.025

Covariances/Correlations/Residual Correlations
U1            U2            U3            U4            U5
________      ________      ________      ________      ________
U1
U2             0.854
U3             0.802         0.855
U4             0.025        -0.070         0.026
U5             0.012        -0.082        -0.037         0.817
U6            -0.007        -0.013        -0.044         0.758         0.841

Covariances/Correlations/Residual Correlations
U6
________

MODEL FIT INFORMATION

Number of Free Parameters                       13

Chi-Square Test of Model Fit

Degrees of freedom                       8

Mean                                 5.482
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       1.000            1.646          5.482
0.980       1.000            2.032          5.482
0.950       1.000            2.733          5.482
0.900       1.000            3.490          5.482
0.800       1.000            4.594          5.482
0.700       0.000            5.527          5.482
0.500       0.000            7.344          5.482
0.300       0.000            9.524          5.482
0.200       0.000           11.030          5.482
0.100       0.000           13.362          5.482
0.050       0.000           15.507          5.482
0.020       0.000           18.168          5.482
0.010       0.000           20.090          5.482

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                                 0.021
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                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
U2                  1.000     1.0673     0.0000     0.0433     0.0045 1.000 1.000
U3                  1.000     1.0008     0.0000     0.0386     0.0000 1.000 1.000

F2       BY
U4                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
U5                  1.000     1.1094     0.0000     0.0542     0.0120 0.000 1.000
U6                  1.000     1.0297     0.0000     0.0468     0.0009 1.000 1.000

F2       WITH
F1                  0.000    -0.0209     0.0000     0.0485     0.0004 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
U4\$1                0.000     0.0602     0.0000     0.0561     0.0036 1.000 0.000
U5\$1                0.000     0.0201     0.0000     0.0561     0.0004 1.000 0.000
U6\$1                0.000     0.0251     0.0000     0.0561     0.0006 1.000 0.000

Variances
F1                  0.800     0.8005     0.0000     0.0459     0.0000 1.000 1.000
F2                  0.800     0.7362     0.0000     0.0522     0.0041 1.000 1.000

QUALITY OF NUMERICAL RESULTS

Average Condition Number for the Information Matrix      0.200E-01
(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
________
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

PSI
F1            F2
________      ________
F1                11
F2                12            13

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
________
0.000

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             1.066         0.000
U3             1.000         0.000
U4             0.000         1.000
U5             0.000         1.109
U6             0.000         1.030

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          U4\$1          U5\$1
________      ________      ________      ________      ________
0.000         0.000         0.000         0.000         0.000

TAU
U6\$1
________
0.000

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             1.000         0.000
U4             0.000         1.000
U5             0.000         1.000
U6             0.000         1.000

THETA
U1            U2            U3            U4            U5
________      ________      ________      ________      ________
U1             0.200
U2             0.000         0.200
U3             0.000         0.000         0.200
U4             0.000         0.000         0.000         0.200
U5             0.000         0.000         0.000         0.000         0.200
U6             0.000         0.000         0.000         0.000         0.000

THETA
U6
________
U6             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
U4
U5
U6

Save file
ex5.2.dat

Save file format           Free
Save file record length    10000

Beginning Time:  22:23:04
Ending Time:  22:23:05
Elapsed Time:  00:00:01

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Copyright (c) 1998-2022 Muthen & Muthen
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