```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, using 4-category
outcomes

montecarlo:
names = u11-u14;
generate = u11-u14(3);
categorical = u11 - u14;
nobs = 500;
nreps = 1;
save = ex6.5.dat;

analysis:
parameterization = theta;

model population:

i s | u11@0 u12@1 u13@2 u14@3;
[u11\$1-u14\$1*-.7];
[u11\$2-u14\$2*0];
[u11\$3-u14\$3*.7];
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*-.7] (1);
[u11\$2-u14\$2*0] (2);
[u11\$3-u14\$3*.7] (3);
u11@.5 u12*.6 u13*.9 u14*1.4;
! in the theta parameterization used here,
! the residual variance needs to be fixed for
! one time point for identification purposes.
! here, it is fixed at the true value for the first
! time point (.5), although in the real-data
! analysis the default is fixed at 1 which makes
! the estimates come out in a different metric
[i@0 s*-.5];
i*.5; s*.1; i with s*0;

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, using 4-category
outcomes

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                                             THETA

SAMPLE STATISTICS FOR THE FIRST REPLICATION

SAMPLE STATISTICS

Means/Intercepts/Thresholds
U11\$1         U11\$2         U11\$3         U12\$1         U12\$2
________      ________      ________      ________      ________
-0.719        -0.040         0.668        -0.285         0.440

Means/Intercepts/Thresholds
U12\$3         U13\$1         U13\$2         U13\$3         U14\$1
________      ________      ________      ________      ________
0.986         0.238         0.595         1.136         0.457

Means/Intercepts/Thresholds
U14\$2         U14\$3
________      ________
0.849         1.237

Covariances/Correlations/Residual Correlations
U11           U12           U13           U14
________      ________      ________      ________
U11
U12            0.506
U13            0.397         0.541
U14            0.303         0.427         0.515

MODEL FIT INFORMATION

Number of Free Parameters                       10

Chi-Square Test of Model Fit

Degrees of freedom                       8

Mean                                12.014
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       1.000            1.646         12.014
0.980       1.000            2.032         12.014
0.950       1.000            2.733         12.014
0.900       1.000            3.490         12.014
0.800       1.000            4.594         12.014
0.700       1.000            5.527         12.014
0.500       1.000            7.344         12.014
0.300       1.000            9.524         12.014
0.200       1.000           11.030         12.014
0.100       0.000           13.362         12.014
0.050       0.000           15.507         12.014
0.020       0.000           18.168         12.014
0.010       0.000           20.090         12.014

RMSEA (Root Mean Square Error Of Approximation)

Mean                                 0.032
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

CFI/TLI

CFI

Mean                                 0.992
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                                 0.994
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

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    -0.0236     0.0000     0.0590     0.0006 1.000 0.000

Means
I                   0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
S                  -0.500    -0.5462     0.0000     0.0760     0.0021 1.000 1.000

Thresholds
U11\$1              -0.700    -0.8090     0.0000     0.1075     0.0119 1.000 1.000
U11\$2               0.000    -0.0502     0.0000     0.0549     0.0025 1.000 0.000
U11\$3               0.700     0.7076     0.0000     0.1011     0.0001 1.000 1.000
U12\$1              -0.700    -0.8090     0.0000     0.1075     0.0119 1.000 1.000
U12\$2               0.000    -0.0502     0.0000     0.0549     0.0025 1.000 0.000
U12\$3               0.700     0.7076     0.0000     0.1011     0.0001 1.000 1.000
U13\$1              -0.700    -0.8090     0.0000     0.1075     0.0119 1.000 1.000
U13\$2               0.000    -0.0502     0.0000     0.0549     0.0025 1.000 0.000
U13\$3               0.700     0.7076     0.0000     0.1011     0.0001 1.000 1.000
U14\$1              -0.700    -0.8090     0.0000     0.1075     0.0119 1.000 1.000
U14\$2               0.000    -0.0502     0.0000     0.0549     0.0025 1.000 0.000
U14\$3               0.700     0.7076     0.0000     0.1011     0.0001 1.000 1.000

Variances
I                   0.500     0.7253     0.0000     0.2501     0.0507 1.000 1.000
S                   0.100     0.1565     0.0000     0.0677     0.0032 1.000 1.000

Residual Variances
U11                 0.500     0.5000     0.0000     0.0000     0.0000 1.000 0.000
U12                 0.600     0.6666     0.0000     0.2042     0.0044 1.000 1.000
U13                 0.900     1.2082     0.0000     0.3439     0.0950 1.000 1.000
U14                 1.400     1.6644     0.0000     0.5026     0.0699 1.000 1.000

QUALITY OF NUMERICAL RESULTS

Average Condition Number for the Information Matrix      0.298E-03
(ratio of smallest to largest eigenvalue)

TECHNICAL OUTPUT

PARAMETER SPECIFICATION

TAU
U11\$1         U11\$2         U11\$3         U12\$1         U12\$2
________      ________      ________      ________      ________
1             2             3             1             2

TAU
U12\$3         U13\$1         U13\$2         U13\$3         U14\$1
________      ________      ________      ________      ________
3             1             2             3             1

TAU
U14\$2         U14\$3
________      ________
2             3

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

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

THETA
U11           U12           U13           U14
________      ________      ________      ________
U11                0
U12                0             4
U13                0             0             5
U14                0             0             0             6

ALPHA
I             S
________      ________
0             7

BETA
I             S
________      ________
I                  0             0
S                  0             0

PSI
I             S
________      ________
I                  8
S                  9            10

STARTING VALUES

TAU
U11\$1         U11\$2         U11\$3         U12\$1         U12\$2
________      ________      ________      ________      ________
-0.700         0.000         0.700        -0.700         0.000

TAU
U12\$3         U13\$1         U13\$2         U13\$3         U14\$1
________      ________      ________      ________      ________
0.700        -0.700         0.000         0.700        -0.700

TAU
U14\$2         U14\$3
________      ________
0.000         0.700

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

POPULATION VALUES

TAU
U11\$1         U11\$2         U11\$3         U12\$1         U12\$2
________      ________      ________      ________      ________
-0.700         0.000         0.700        -0.700         0.000

TAU
U12\$3         U13\$1         U13\$2         U13\$3         U14\$1
________      ________      ________      ________      ________
0.700        -0.700         0.000         0.700        -0.700

TAU
U14\$2         U14\$3
________      ________
0.000         0.700

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
ex6.5.dat

Save file format           Free
Save file record length    10000

Beginning Time:  22:24:25
Ending Time:  22:24:26
Elapsed Time:  00:00:01

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