```Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   3:27 AM

INPUT INSTRUCTIONS

TITLE:	this is an example of a path analysis
with categorical dependent variables
using the theta parameterization
MONTECARLO:
NAMES = u1-u3 x1-x3;
NOBSERVATIONS = 1000;
NREPS = 1;
SEED = 53487;
GENERATE = u1(2) u2(1) u3(3);
CATEGORICAL = u1-u3;
SAVE = ex3.13.dat;
MODEL POPULATION:
[x1-x3@0];
x1-x3@1;
u1 ON x1*3 x2*2 x3*1;
u2 ON x1*1 x2*2 x3*3;
u3 ON u1*1 u2*-1 x2*2;
[u1\$1*-1 u1\$2*1];
[u2\$1*0];
[u3\$1*-.5 u3\$2*.5 u3\$3*1.5];
u1-u3*1;
ANALYSIS:
PARAMETERIZATION = THETA;
MODEL:
u1 ON x1*3 x2*2 x3*1;
u2 ON x1*1 x2*2 x3*3;
u3 ON u1*1 u2*-1 x2*2;
[u1\$1*-1 u1\$2*1];
[u2\$1*0];
[u3\$1*-.5 u3\$2*.5 u3\$3*1.5];
OUTPUT:	TECH9;

this is an example of a path analysis
with categorical dependent variables
using the theta parameterization

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                        1000

Number of replications
Requested                                                    1
Completed                                                    1
Value of seed                                                53487

Number of dependent variables                                    3
Number of independent variables                                  3
Number of continuous latent variables                            0

Observed dependent variables

Binary and ordered categorical (ordinal)
U1          U2          U3

Observed independent variables
X1          X2          X3

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
U1\$1          U1\$2          U2\$1          U3\$1          U3\$2
________      ________      ________      ________      ________
-0.957         1.109         0.064        -0.360         0.288

Means/Intercepts/Thresholds
U3\$3
________
0.879

Slopes
X1            X2            X3
________      ________      ________
U1             2.965         1.926         1.050
U2             1.027         2.084         3.025
U3             1.179         1.205        -1.215

Covariances/Correlations/Residual Correlations
U1            U2            U3
________      ________      ________
U1
U2             0.062
U3             0.655        -0.347

MODEL FIT INFORMATION

Number of Free Parameters                       15

Chi-Square Test of Model Fit

Degrees of freedom                       3

Mean                                 6.871
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       1.000            0.115          6.871
0.980       1.000            0.185          6.871
0.950       1.000            0.352          6.871
0.900       1.000            0.584          6.871
0.800       1.000            1.005          6.871
0.700       1.000            1.424          6.871
0.500       1.000            2.366          6.871
0.300       1.000            3.665          6.871
0.200       1.000            4.642          6.871
0.100       1.000            6.251          6.871
0.050       0.000            7.815          6.871
0.020       0.000            9.837          6.871
0.010       0.000           11.345          6.871

RMSEA (Root Mean Square Error Of Approximation)

Mean                                 0.036
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000            0.036          0.036
0.980       0.000            0.036          0.036
0.950       0.000            0.036          0.036
0.900       0.000            0.036          0.036
0.800       0.000            0.036          0.036
0.700       0.000            0.036          0.036
0.500       0.000            0.036          0.036
0.300       0.000            0.036          0.036
0.200       0.000            0.036          0.036
0.100       0.000            0.036          0.036
0.050       0.000            0.036          0.036
0.020       0.000            0.036          0.036
0.010       0.000            0.036          0.036

WRMR (Weighted Root Mean Square Residual)

Mean                                 0.612
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000            0.612          0.612
0.980       0.000            0.612          0.612
0.950       0.000            0.612          0.612
0.900       0.000            0.612          0.612
0.800       0.000            0.612          0.612
0.700       0.000            0.612          0.612
0.500       0.000            0.612          0.612
0.300       0.000            0.612          0.612
0.200       0.000            0.612          0.612
0.100       0.000            0.612          0.612
0.050       0.000            0.612          0.612
0.020       0.000            0.612          0.612
0.010       0.000            0.612          0.612

MODEL RESULTS

ESTIMATES              S. E.     M. S. E.  95%  % Sig
Population   Average   Std. Dev.   Average             Cover Coeff
U1       ON
X1                  3.000     2.9176     0.0000     0.1524     0.0068 1.000 1.000
X2                  2.000     1.9258     0.0000     0.1032     0.0055 1.000 1.000
X3                  1.000     1.0300     0.0000     0.0765     0.0009 1.000 1.000

U2       ON
X1                  1.000     1.0456     0.0000     0.1053     0.0021 1.000 1.000
X2                  2.000     2.0840     0.0000     0.1750     0.0071 1.000 1.000
X3                  3.000     3.2132     0.0000     0.2298     0.0455 1.000 1.000

U3       ON
U1                  1.000     1.1088     0.0000     0.1839     0.0118 1.000 1.000
U2                 -1.000    -1.0263     0.0000     0.1954     0.0007 1.000 1.000
X2                  2.000     2.1869     0.0000     0.3233     0.0349 1.000 1.000

Thresholds
U1\$1               -1.000    -0.9571     0.0000     0.0812     0.0018 1.000 1.000
U1\$2                1.000     1.1093     0.0000     0.0869     0.0119 1.000 1.000
U2\$1                0.000     0.0642     0.0000     0.0798     0.0041 1.000 0.000
U3\$1               -0.500    -0.6529     0.0000     0.1271     0.0234 1.000 1.000
U3\$2                0.500     0.5223     0.0000     0.1238     0.0005 1.000 1.000
U3\$3                1.500     1.5925     0.0000     0.2250     0.0086 1.000 1.000

QUALITY OF NUMERICAL RESULTS

Average Condition Number for the Information Matrix      0.172E-02
(ratio of smallest to largest eigenvalue)

TECHNICAL OUTPUT

PARAMETER SPECIFICATION

TAU
U1\$1          U1\$2          U2\$1          U3\$1          U3\$2
________      ________      ________      ________      ________
1             2             3             4             5

TAU
U3\$3
________
6

NU
U1            U2            U3
________      ________      ________
0             0             0

LAMBDA
U1            U2            U3
________      ________      ________
U1                 0             0             0
U2                 0             0             0
U3                 0             0             0

THETA
U1            U2            U3
________      ________      ________
U1                 0
U2                 0             0
U3                 0             0             0

ALPHA
U1            U2            U3
________      ________      ________
0             0             0

BETA
U1            U2            U3
________      ________      ________
U1                 0             0             0
U2                 0             0             0
U3                 7             8             0

GAMMA
X1            X2            X3
________      ________      ________
U1                 9            10            11
U2                12            13            14
U3                 0            15             0

PSI
U1            U2            U3
________      ________      ________
U1                 0
U2                 0             0
U3                 0             0             0

STARTING VALUES

TAU
U1\$1          U1\$2          U2\$1          U3\$1          U3\$2
________      ________      ________      ________      ________
-1.000         1.000         0.000        -0.500         0.500

TAU
U3\$3
________
1.500

NU
U1            U2            U3
________      ________      ________
0.000         0.000         0.000

LAMBDA
U1            U2            U3
________      ________      ________
U1             1.000         0.000         0.000
U2             0.000         1.000         0.000
U3             0.000         0.000         1.000

THETA
U1            U2            U3
________      ________      ________
U1             0.000
U2             0.000         0.000
U3             0.000         0.000         0.000

ALPHA
U1            U2            U3
________      ________      ________
0.000         0.000         0.000

BETA
U1            U2            U3
________      ________      ________
U1             0.000         0.000         0.000
U2             0.000         0.000         0.000
U3             1.000        -1.000         0.000

GAMMA
X1            X2            X3
________      ________      ________
U1             3.000         2.000         1.000
U2             1.000         2.000         3.000
U3             0.000         2.000         0.000

PSI
U1            U2            U3
________      ________      ________
U1             1.000
U2             0.000         1.000
U3             0.000         0.000         1.000

POPULATION VALUES

TAU
U1\$1          U1\$2          U2\$1          U3\$1          U3\$2
________      ________      ________      ________      ________
-1.000         1.000         0.000        -0.500         0.500

TAU
U3\$3
________
1.500

NU
U1            U2            U3            X1            X2
________      ________      ________      ________      ________
0.000         0.000         0.000         0.000         0.000

NU
X3
________
0.000

LAMBDA
U1            U2            U3            X1            X2
________      ________      ________      ________      ________
U1             1.000         0.000         0.000         0.000         0.000
U2             0.000         1.000         0.000         0.000         0.000
U3             0.000         0.000         1.000         0.000         0.000
X1             0.000         0.000         0.000         1.000         0.000
X2             0.000         0.000         0.000         0.000         1.000
X3             0.000         0.000         0.000         0.000         0.000

LAMBDA
X3
________
U1             0.000
U2             0.000
U3             0.000
X1             0.000
X2             0.000
X3             1.000

THETA
U1            U2            U3            X1            X2
________      ________      ________      ________      ________
U1             0.000
U2             0.000         0.000
U3             0.000         0.000         0.000
X1             0.000         0.000         0.000         0.000
X2             0.000         0.000         0.000         0.000         0.000
X3             0.000         0.000         0.000         0.000         0.000

THETA
X3
________
X3             0.000

ALPHA
U1            U2            U3            X1            X2
________      ________      ________      ________      ________
0.000         0.000         0.000         0.000         0.000

ALPHA
X3
________
0.000

BETA
U1            U2            U3            X1            X2
________      ________      ________      ________      ________
U1             0.000         0.000         0.000         3.000         2.000
U2             0.000         0.000         0.000         1.000         2.000
U3             1.000        -1.000         0.000         0.000         2.000
X1             0.000         0.000         0.000         0.000         0.000
X2             0.000         0.000         0.000         0.000         0.000
X3             0.000         0.000         0.000         0.000         0.000

BETA
X3
________
U1             1.000
U2             3.000
U3             0.000
X1             0.000
X2             0.000
X3             0.000

PSI
U1            U2            U3            X1            X2
________      ________      ________      ________      ________
U1             1.000
U2             0.000         1.000
U3             0.000         0.000         1.000
X1             0.000         0.000         0.000         1.000
X2             0.000         0.000         0.000         0.000         1.000
X3             0.000         0.000         0.000         0.000         0.000

PSI
X3
________
X3             1.000

TECHNICAL 9 OUTPUT

Error messages for each replication (if any)

SAVEDATA INFORMATION

Order of variables

U1
U2
U3
X1
X2
X3

Save file
ex3.13.dat

Save file format           Free
Save file record length    10000

Beginning Time:  03:27:49
Ending Time:  03:27:49
Elapsed Time:  00:00:00

MUTHEN & MUTHEN
3463 Stoner Ave.
Los Angeles, CA  90066

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

Copyright (c) 1998-2017 Muthen & Muthen
```