```Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022  10:24 PM

INPUT INSTRUCTIONS

title:		this is an example of a linear growth
model for a categorical outcome
This is the same example as in section 9.2 of
Mplus Web Note #4, page 18

montecarlo:
names = u11-u14;
generate = u11-u14(1);
categorical = u11 - u14;
nobs = 500;
nreps = 1;
save = ex6.4.dat;

model population:

i s | u11@0 u12@1 u13@2 u14@3;
[u11\$1-u14\$1*-.5] (1);
u11*.5 u12*.6 u13*.9 u14*1.4;
[i@0 s*-.5];
i*.5; s*.1; i with s*0;

model:

i s | u11@0 u12@1 u13@2 u14@3;
[u11\$1-u14\$1*-.5] (1);
! residual variances are not part of the
! default WLSMV Delta parameterization
[i@0 s*-.5];
i*.5; s*.1; i with s*0;
{u11@1 u12*.913 u13*.745 u14*.598};
! this sets the scale factors at the inverted SDs
! for the u* variables, so that the estimates
! are in the metric of the Delta
! parametrizations

output:
tech9;

this is an example of a linear growth
model for a categorical outcome
This is the same example as in section 9.2 of
Mplus Web Note #4, page 18

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                                    4
Number of independent variables                                  0
Number of continuous latent variables                            2

Observed dependent variables

Binary and ordered categorical (ordinal)
U11         U12         U13         U14

Continuous latent variables
I           S

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
U11\$1         U12\$1         U13\$1         U14\$1
________      ________      ________      ________
-0.496        -0.085         0.316         0.565

Covariances/Correlations/Residual Correlations
U11           U12           U13           U14
________      ________      ________      ________
U11
U12            0.463
U13            0.399         0.554
U14            0.354         0.406         0.517

MODEL FIT INFORMATION

Number of Free Parameters                        8

Chi-Square Test of Model Fit

Degrees of freedom                       2

Mean                                 1.214
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       1.000            0.020          1.214
0.980       1.000            0.040          1.214
0.950       1.000            0.103          1.214
0.900       1.000            0.211          1.214
0.800       1.000            0.446          1.214
0.700       1.000            0.713          1.214
0.500       0.000            1.386          1.214
0.300       0.000            2.408          1.214
0.200       0.000            3.219          1.214
0.100       0.000            4.605          1.214
0.050       0.000            5.991          1.214
0.020       0.000            7.824          1.214
0.010       0.000            9.210          1.214

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                                 0.016
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

I        |
U11                 1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
U12                 1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
U13                 1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
U14                 1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000

S        |
U11                 0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
U12                 1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
U13                 2.000     2.0000     0.0000     0.0000     0.0000 1.000 0.000
U14                 3.000     3.0000     0.0000     0.0000     0.0000 1.000 0.000

I        WITH
S                   0.000    -0.0071     0.0000     0.0537     0.0001 1.000 0.000

Means
I                   0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
S                  -0.500    -0.4068     0.0000     0.0530     0.0087 1.000 1.000

Thresholds
U11\$1              -0.500    -0.4935     0.0000     0.0580     0.0000 1.000 1.000
U12\$1              -0.500    -0.4935     0.0000     0.0580     0.0000 1.000 1.000
U13\$1              -0.500    -0.4935     0.0000     0.0580     0.0000 1.000 1.000
U14\$1              -0.500    -0.4935     0.0000     0.0580     0.0000 1.000 1.000

Variances
I                   0.500     0.4389     0.0000     0.1142     0.0037 1.000 1.000
S                   0.100     0.0420     0.0000     0.0350     0.0034 1.000 0.000

Scales
U11                 1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
U12                 0.913     1.0598     0.0000     0.1486     0.0215 1.000 1.000
U13                 0.745     1.0116     0.0000     0.1924     0.0711 1.000 1.000
U14                 0.598     0.7719     0.0000     0.1535     0.0302 1.000 1.000

QUALITY OF NUMERICAL RESULTS

Average Condition Number for the Information Matrix      0.496E-03
(ratio of smallest to largest eigenvalue)

TECHNICAL OUTPUT

PARAMETER SPECIFICATION

TAU
U11\$1         U12\$1         U13\$1         U14\$1
________      ________      ________      ________
1             1             1             1

NU
U11           U12           U13           U14
________      ________      ________      ________
0             0             0             0

LAMBDA
I             S
________      ________
U11                0             0
U12                0             0
U13                0             0
U14                0             0

ALPHA
I             S
________      ________
0             2

BETA
I             S
________      ________
I                  0             0
S                  0             0

PSI
I             S
________      ________
I                  3
S                  4             5

DELTA
U11           U12           U13           U14
________      ________      ________      ________
0             6             7             8

STARTING VALUES

TAU
U11\$1         U12\$1         U13\$1         U14\$1
________      ________      ________      ________
-0.500        -0.500        -0.500        -0.500

NU
U11           U12           U13           U14
________      ________      ________      ________
0.000         0.000         0.000         0.000

LAMBDA
I             S
________      ________
U11            1.000         0.000
U12            1.000         1.000
U13            1.000         2.000
U14            1.000         3.000

ALPHA
I             S
________      ________
0.000        -0.500

BETA
I             S
________      ________
I              0.000         0.000
S              0.000         0.000

PSI
I             S
________      ________
I              0.500
S              0.000         0.100

DELTA
U11           U12           U13           U14
________      ________      ________      ________
1.000         0.913         0.745         0.598

POPULATION VALUES

TAU
U11\$1         U12\$1         U13\$1         U14\$1
________      ________      ________      ________
-0.500        -0.500        -0.500        -0.500

NU
U11           U12           U13           U14
________      ________      ________      ________
0.000         0.000         0.000         0.000

LAMBDA
I             S
________      ________
U11            1.000         0.000
U12            1.000         1.000
U13            1.000         2.000
U14            1.000         3.000

THETA
U11           U12           U13           U14
________      ________      ________      ________
U11            0.500
U12            0.000         0.600
U13            0.000         0.000         0.900
U14            0.000         0.000         0.000         1.400

ALPHA
I             S
________      ________
0.000        -0.500

BETA
I             S
________      ________
I              0.000         0.000
S              0.000         0.000

PSI
I             S
________      ________
I              0.500
S              0.000         0.100

TECHNICAL 9 OUTPUT

Error messages for each replication (if any)

SAVEDATA INFORMATION

Order of variables

U11
U12
U13
U14

Save file
ex6.4.dat

Save file format           Free
Save file record length    10000

Beginning Time:  22:24:25
Ending Time:  22:24:25
Elapsed Time:  00:00:00

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Copyright (c) 1998-2022 Muthen & Muthen
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