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

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 = ex5.22.dat;

model population:
[u1\$1-u2\$1*0];
u1-u2@1; ! u* variances are fixed at 1 by default in
! the analysis
u1 WITH u2*0.73; ! Value for MZ twins

model population-g2:
u1 WITH u2*0.41;  ! Value for DZ twins

model:
[u1\$1-u2\$1*0](1);
u1 WITH u2*0.73(covmz);

model g2:
u1 WITH u2*0.41(covdz);

model constraint:
NEW(a*.8 c*.3 h*.64);
! e is not a free parameter but obtained as 1 - (a**2 + c**2)
covmz = a**2 + c**2;
covdz = 0.5*a**2 + c**2;
h = a**2/1;

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                            0

Observed dependent variables

Binary and ordered categorical (ordinal)
U1          U2

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

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                                 0.005
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

MODEL RESULTS

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

Group G1

U1       WITH
U2                  0.730     0.7707     0.0000     0.0262     0.0017 1.000 1.000

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

Group G2

U1       WITH
U2                  0.410     0.4114     0.0000     0.0436     0.0000 1.000 1.000

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

A                   0.800     0.8477     0.0000     0.0600     0.0023 1.000 1.000
C                   0.300     0.2284     0.0000     0.1993     0.0051 1.000 0.000
H                   0.640     0.7185     0.0000     0.1018     0.0062 1.000 1.000

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

THETA
U1            U2
________      ________
U1                 0
U2                 2             0

DELTA
U1            U2
________      ________
0             0

PARAMETER SPECIFICATION FOR G2

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

NU
U1            U2
________      ________
0             0

THETA
U1            U2
________      ________
U1                 0
U2                 3             0

DELTA
U1            U2
________      ________
0             0

PARAMETER SPECIFICATION FOR THE ADDITIONAL PARAMETERS

A             C             H
________      ________      ________
4             5             6

STARTING VALUES FOR G1

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

NU
U1            U2
________      ________
0.000         0.000

THETA
U1            U2
________      ________
U1             1.000
U2             0.730         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

THETA
U1            U2
________      ________
U1             1.000
U2             0.410         1.000

DELTA
U1            U2
________      ________
1.000         1.000

STARTING VALUES FOR THE ADDITIONAL PARAMETERS

A             C             H
________      ________      ________
0.800         0.300         0.640

POPULATION VALUES FOR G1

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

NU
U1            U2
________      ________
0.000         0.000

THETA
U1            U2
________      ________
U1             1.000
U2             0.730         1.000

POPULATION VALUES FOR G2

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

NU
U1            U2
________      ________
0.000         0.000

THETA
U1            U2
________      ________
U1             1.000
U2             0.410         1.000

TECHNICAL 9 OUTPUT

Error messages for each replication (if any)

SAVEDATA INFORMATION

Order of variables

U1
U2
GROUP

Save file
ex5.22.dat

Save file format           Free
Save file record length    10000

Beginning Time:  22:23:05
Ending Time:  22:23:06
Elapsed Time:  00:00:01

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