```Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   3:28 AM

INPUT INSTRUCTIONS

title:	this is an example of a 2-group twin model
for a categorical outcome using probit WLSMV

montecarlo:
names = u1 u2;
ngroups = 2;
nobs = 1000 1000;
generate = u1-u2(1);
categorical = u1 u2;
nreps = 1;
save = ex5.19.dat;

model population:
[u1\$1-u2\$1*0] (1);
a1 BY u1*.8 (2);
a2 BY u2*.8 (2);
c1 BY u1*.3 (3);
c2 BY u2*.3 (3);
! e**2 is a residual variance and not a
! free parameter for categorical outcomes.
! Because the y* variance is 1, e**2 = .27
u1-u2@.27;
a1-c2@1;
[a1-c2@0];
a1 WITH a2@1; ! value for MZ twins
c1 WITH c2@1;
a1 WITH c1-c2@0;
a2 WITH c1-c2@0;

model population-g2:
a1 WITH a2@.5;  ! Value for DZ twins

model:
[u1\$1-u2\$1*0] (1);
a1 BY u1*.8 (2);
a2 BY u2*.8 (2);
c1 BY u1*.3 (3);
c2 BY u2*.3 (3);
! e**2 is a residual variance and not a
! free parameter for categorical outcomes.
! Because the y* variance is 1, e**2 = .27
a1-c2@1;
[a1-c2@0];
a1 WITH a2@1; ! value for MZ twins
c1 WITH c2@1;
a1 WITH c1-c2@0;
a2 WITH c1-c2@0;

model g2:
a1 WITH a2@.5;  ! Value for DZ twins
{u1-u2@1};

output:
tech9;

this is an example of a 2-group twin model
for a categorical outcome using probit WLSMV

SUMMARY OF ANALYSIS

Number of groups                                                 2
Number of observations
Group G1                                                   1000
Group G2                                                   1000
Total sample size                                          2000

Number of replications
Requested                                                    1
Completed                                                    1
Value of seed                                                    0

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

Observed dependent variables

Binary and ordered categorical (ordinal)
U1          U2

Continuous latent variables
A1          A2          C1          C2

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 FOR G1

Means/Intercepts/Thresholds
U1\$1          U2\$1
________      ________
0.005        -0.015

Covariances/Correlations/Residual Correlations
U1            U2
________      ________
U1
U2             0.771

SAMPLE STATISTICS FOR G2

Means/Intercepts/Thresholds
U1\$1          U2\$1
________      ________
0.010         0.028

Covariances/Correlations/Residual Correlations
U1            U2
________      ________
U1
U2             0.411

MODEL FIT INFORMATION

Number of Free Parameters                        3

Chi-Square Test of Model Fit

Degrees of freedom                       3

Mean                                 0.905
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       1.000            0.115          0.905
0.980       1.000            0.185          0.905
0.950       1.000            0.352          0.905
0.900       1.000            0.584          0.905
0.800       0.000            1.005          0.905
0.700       0.000            1.424          0.905
0.500       0.000            2.366          0.905
0.300       0.000            3.665          0.905
0.200       0.000            4.642          0.905
0.100       0.000            6.251          0.905
0.050       0.000            7.815          0.905
0.020       0.000            9.837          0.905
0.010       0.000           11.345          0.905

RMSEA (Root Mean Square Error Of Approximation)

Mean                                 0.000
Std Dev                              0.000
Number of successful computations        1

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

WRMR (Weighted Root Mean Square Residual)

Mean                                 0.442
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000            0.442          0.442
0.980       0.000            0.442          0.442
0.950       0.000            0.442          0.442
0.900       0.000            0.442          0.442
0.800       0.000            0.442          0.442
0.700       0.000            0.442          0.442
0.500       0.000            0.442          0.442
0.300       0.000            0.442          0.442
0.200       0.000            0.442          0.442
0.100       0.000            0.442          0.442
0.050       0.000            0.442          0.442
0.020       0.000            0.442          0.442
0.010       0.000            0.442          0.442

MODEL RESULTS

ESTIMATES              S. E.     M. S. E.  95%  % Sig
Population   Average   Std. Dev.   Average             Cover Coeff
Group G1

A1       BY
U1                  0.800     0.8477     0.0000     0.0600     0.0023 1.000 1.000

A2       BY
U2                  0.800     0.8477     0.0000     0.0600     0.0023 1.000 1.000

C1       BY
U1                  0.300     0.2284     0.0000     0.1993     0.0051 1.000 0.000

C2       BY
U2                  0.300     0.2284     0.0000     0.1993     0.0051 1.000 0.000

A1       WITH
A2                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
C1                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
C2                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

C1       WITH
C2                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
A2                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

A2       WITH
C2                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

Means
A1                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
A2                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
C1                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
C2                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

Thresholds
U1\$1                0.000     0.0069     0.0000     0.0236     0.0000 1.000 0.000
U2\$1                0.000     0.0069     0.0000     0.0236     0.0000 1.000 0.000

Variances
A1                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
A2                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
C1                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
C2                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000

Scales
U1                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
U2                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000

Group G2

A1       BY
U1                  0.800     0.8477     0.0000     0.0600     0.0023 1.000 1.000

A2       BY
U2                  0.800     0.8477     0.0000     0.0600     0.0023 1.000 1.000

C1       BY
U1                  0.300     0.2284     0.0000     0.1993     0.0051 1.000 0.000

C2       BY
U2                  0.300     0.2284     0.0000     0.1993     0.0051 1.000 0.000

A1       WITH
A2                  0.500     0.5000     0.0000     0.0000     0.0000 1.000 0.000
C1                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
C2                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

C1       WITH
C2                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
A2                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

A2       WITH
C2                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

Means
A1                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
A2                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
C1                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
C2                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

Thresholds
U1\$1                0.000     0.0069     0.0000     0.0236     0.0000 1.000 0.000
U2\$1                0.000     0.0069     0.0000     0.0236     0.0000 1.000 0.000

Variances
A1                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
A2                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
C1                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
C2                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000

Scales
U1                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
U2                  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      0.469E-02
(ratio of smallest to largest eigenvalue)

TECHNICAL OUTPUT

PARAMETER SPECIFICATION FOR G1

TAU
U1\$1          U2\$1
________      ________
1             1

NU
U1            U2
________      ________
0             0

LAMBDA
A1            A2            C1            C2
________      ________      ________      ________
U1                 2             0             3             0
U2                 0             2             0             3

ALPHA
A1            A2            C1            C2
________      ________      ________      ________
0             0             0             0

BETA
A1            A2            C1            C2
________      ________      ________      ________
A1                 0             0             0             0
A2                 0             0             0             0
C1                 0             0             0             0
C2                 0             0             0             0

PSI
A1            A2            C1            C2
________      ________      ________      ________
A1                 0
A2                 0             0
C1                 0             0             0
C2                 0             0             0             0

DELTA
U1            U2
________      ________
0             0

PARAMETER SPECIFICATION FOR G2

TAU
U1\$1          U2\$1
________      ________
1             1

NU
U1            U2
________      ________
0             0

LAMBDA
A1            A2            C1            C2
________      ________      ________      ________
U1                 2             0             3             0
U2                 0             2             0             3

ALPHA
A1            A2            C1            C2
________      ________      ________      ________
0             0             0             0

BETA
A1            A2            C1            C2
________      ________      ________      ________
A1                 0             0             0             0
A2                 0             0             0             0
C1                 0             0             0             0
C2                 0             0             0             0

PSI
A1            A2            C1            C2
________      ________      ________      ________
A1                 0
A2                 0             0
C1                 0             0             0
C2                 0             0             0             0

DELTA
U1            U2
________      ________
0             0

STARTING VALUES FOR G1

TAU
U1\$1          U2\$1
________      ________
0.000         0.000

NU
U1            U2
________      ________
0.000         0.000

LAMBDA
A1            A2            C1            C2
________      ________      ________      ________
U1             0.800         0.000         0.300         0.000
U2             0.000         0.800         0.000         0.300

ALPHA
A1            A2            C1            C2
________      ________      ________      ________
0.000         0.000         0.000         0.000

BETA
A1            A2            C1            C2
________      ________      ________      ________
A1             0.000         0.000         0.000         0.000
A2             0.000         0.000         0.000         0.000
C1             0.000         0.000         0.000         0.000
C2             0.000         0.000         0.000         0.000

PSI
A1            A2            C1            C2
________      ________      ________      ________
A1             1.000
A2             1.000         1.000
C1             0.000         0.000         1.000
C2             0.000         0.000         1.000         1.000

DELTA
U1            U2
________      ________
1.000         1.000

STARTING VALUES FOR G2

TAU
U1\$1          U2\$1
________      ________
0.000         0.000

NU
U1            U2
________      ________
0.000         0.000

LAMBDA
A1            A2            C1            C2
________      ________      ________      ________
U1             0.800         0.000         0.300         0.000
U2             0.000         0.800         0.000         0.300

ALPHA
A1            A2            C1            C2
________      ________      ________      ________
0.000         0.000         0.000         0.000

BETA
A1            A2            C1            C2
________      ________      ________      ________
A1             0.000         0.000         0.000         0.000
A2             0.000         0.000         0.000         0.000
C1             0.000         0.000         0.000         0.000
C2             0.000         0.000         0.000         0.000

PSI
A1            A2            C1            C2
________      ________      ________      ________
A1             1.000
A2             0.500         1.000
C1             0.000         0.000         1.000
C2             0.000         0.000         1.000         1.000

DELTA
U1            U2
________      ________
1.000         1.000

POPULATION VALUES FOR G1

TAU
U1\$1          U2\$1
________      ________
0.000         0.000

NU
U1            U2
________      ________
0.000         0.000

LAMBDA
A1            A2            C1            C2
________      ________      ________      ________
U1             0.800         0.000         0.300         0.000
U2             0.000         0.800         0.000         0.300

THETA
U1            U2
________      ________
U1             0.270
U2             0.000         0.270

ALPHA
A1            A2            C1            C2
________      ________      ________      ________
0.000         0.000         0.000         0.000

BETA
A1            A2            C1            C2
________      ________      ________      ________
A1             0.000         0.000         0.000         0.000
A2             0.000         0.000         0.000         0.000
C1             0.000         0.000         0.000         0.000
C2             0.000         0.000         0.000         0.000

PSI
A1            A2            C1            C2
________      ________      ________      ________
A1             1.000
A2             1.000         1.000
C1             0.000         0.000         1.000
C2             0.000         0.000         1.000         1.000

POPULATION VALUES FOR G2

TAU
U1\$1          U2\$1
________      ________
0.000         0.000

NU
U1            U2
________      ________
0.000         0.000

LAMBDA
A1            A2            C1            C2
________      ________      ________      ________
U1             0.800         0.000         0.300         0.000
U2             0.000         0.800         0.000         0.300

THETA
U1            U2
________      ________
U1             0.270
U2             0.000         0.270

ALPHA
A1            A2            C1            C2
________      ________      ________      ________
0.000         0.000         0.000         0.000

BETA
A1            A2            C1            C2
________      ________      ________      ________
A1             0.000         0.000         0.000         0.000
A2             0.000         0.000         0.000         0.000
C1             0.000         0.000         0.000         0.000
C2             0.000         0.000         0.000         0.000

PSI
A1            A2            C1            C2
________      ________      ________      ________
A1             1.000
A2             0.500         1.000
C1             0.000         0.000         1.000
C2             0.000         0.000         1.000         1.000

TECHNICAL 9 OUTPUT

Error messages for each replication (if any)

REPLICATION 1:
WARNING:  THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IN GROUP G1
IS NOT POSITIVE DEFINITE.  THIS COULD INDICATE A NEGATIVE VARIANCE/
RESIDUAL VARIANCE FOR A LATENT VARIABLE, A CORRELATION GREATER OR EQUAL
TO ONE BETWEEN TWO LATENT VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE
PROBLEM INVOLVING VARIABLE A2.

REPLICATION 1:
WARNING:  THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IN GROUP G2
IS NOT POSITIVE DEFINITE.  THIS COULD INDICATE A NEGATIVE VARIANCE/
RESIDUAL VARIANCE FOR A LATENT VARIABLE, A CORRELATION GREATER OR EQUAL
TO ONE BETWEEN TWO LATENT VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE
PROBLEM INVOLVING VARIABLE C2.

SAVEDATA INFORMATION

Order of variables

U1
U2
GROUP

Save file
ex5.19.dat

Save file format           Free
Save file record length    10000

Beginning Time:  03:28:09
Ending Time:  03:28:09
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
```