```Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   3:30 AM

INPUT INSTRUCTIONS

TITLE:	this is an example of a two-level growth model
for a categorical outcome (three-level analysis).

montecarlo:
names are u1-u4 x w;
generate = u1-u4(1);
categorical = u1-u4;
nobservations = 500;
ncsizes = 3;
csizes = 10 (5) 50 (3) 30 (10);
seed = 58459;
nreps = 1;
within = x;
between = w;
save = ex9.13.dat;

ANALYSIS:
TYPE = TWOLEVEL;
integration = 7;

MODEL POPULATION:

%WITHIN%
x@1;
iw sw | u1@0 u2@1 u3@2 u4@3;
iw ON x*1;
sw ON x*.2;
iw*1; sw*.5;

%BETWEEN%
w@1;
ib sb | u1@0 u2@1 u3@2 u4@3;
[u1\$1-u4\$1*0];
ib ON w*.5;
sb ON w*.2;
[ib@0 sb*.5];
ib*.5; sb*.3;

MODEL:

%WITHIN%

iw sw | u1@0 u2@1 u3@2 u4@3;
iw ON x*1;
sw ON x*.2;
iw*1; sw*.5;

%BETWEEN%

ib sb | u1@0 u2@1 u3@2 u4@3;
[u1\$1-u4\$1*0] (1);
ib ON w*.5;
sb ON w*.2;
[ib@0 sb*.5];
ib*.5; sb*.3;

output:
tech8 tech9;

this is an example of a two-level growth model
for a categorical outcome (three-level analysis).

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         500

Number of replications
Requested                                                    1
Completed                                                    1
Value of seed                                                58459

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

Observed dependent variables

Binary and ordered categorical (ordinal)
U1          U2          U3          U4

Observed independent variables
X           W

Continuous latent variables
IW          SW          IB          SB

Variables with special functions

Within variables
X

Between variables
W

Estimator                                                      MLR
Information matrix                                        OBSERVED
Optimization Specifications for the Quasi-Newton Algorithm for
Continuous Outcomes
Maximum number of iterations                                 100
Convergence criterion                                  0.100D-05
Optimization Specifications for the EM Algorithm
Maximum number of iterations                                 500
Convergence criteria
Loglikelihood change                                 0.100D-02
Relative loglikelihood change                        0.100D-05
Derivative                                           0.100D-02
Optimization Specifications for the M step of the EM Algorithm for
Categorical Latent variables
Number of M step iterations                                    1
M step convergence criterion                           0.100D-02
Basis for M step termination                           ITERATION
Optimization Specifications for the M step of the EM Algorithm for
Censored, Binary or Ordered Categorical (Ordinal), Unordered
Categorical (Nominal) and Count Outcomes
Number of M step iterations                                    1
M step convergence criterion                           0.100D-02
Basis for M step termination                           ITERATION
Maximum value for logit thresholds                            15
Minimum value for logit thresholds                           -15
Minimum expected cell size for chi-square              0.100D-01
Optimization algorithm                                         EMA
Integration Specifications
Type                                                    STANDARD
Number of integration points                                   7
Dimensions of numerical integration                            4
Cholesky                                                        ON

SUMMARY OF DATA FOR THE FIRST REPLICATION

Cluster information

Size (s)    Number of clusters of Size s

3            50
5            10
10            30

SAMPLE STATISTICS FOR THE FIRST REPLICATION

SAMPLE STATISTICS

Means
X             W
________      ________
0.030         0.068

Covariances
X             W
________      ________
X              1.048
W              0.042         1.220

Correlations
X             W
________      ________
X              1.000
W              0.037         1.000

MODEL FIT INFORMATION

Number of Free Parameters                       12

Loglikelihood

H0 Value

Mean                             -1053.648
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000        -1053.648      -1053.648
0.980       0.000        -1053.648      -1053.648
0.950       0.000        -1053.648      -1053.648
0.900       0.000        -1053.648      -1053.648
0.800       0.000        -1053.648      -1053.648
0.700       0.000        -1053.648      -1053.648
0.500       0.000        -1053.648      -1053.648
0.300       0.000        -1053.648      -1053.648
0.200       0.000        -1053.648      -1053.648
0.100       0.000        -1053.648      -1053.648
0.050       0.000        -1053.648      -1053.648
0.020       0.000        -1053.648      -1053.648
0.010       0.000        -1053.648      -1053.648

Information Criteria

Akaike (AIC)

Mean                              2131.295
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000         2131.295       2131.295
0.980       0.000         2131.295       2131.295
0.950       0.000         2131.295       2131.295
0.900       0.000         2131.295       2131.295
0.800       0.000         2131.295       2131.295
0.700       0.000         2131.295       2131.295
0.500       0.000         2131.295       2131.295
0.300       0.000         2131.295       2131.295
0.200       0.000         2131.295       2131.295
0.100       0.000         2131.295       2131.295
0.050       0.000         2131.295       2131.295
0.020       0.000         2131.295       2131.295
0.010       0.000         2131.295       2131.295

Bayesian (BIC)

Mean                              2181.871
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000         2181.871       2181.871
0.980       0.000         2181.871       2181.871
0.950       0.000         2181.871       2181.871
0.900       0.000         2181.871       2181.871
0.800       0.000         2181.871       2181.871
0.700       0.000         2181.871       2181.871
0.500       0.000         2181.871       2181.871
0.300       0.000         2181.871       2181.871
0.200       0.000         2181.871       2181.871
0.100       0.000         2181.871       2181.871
0.050       0.000         2181.871       2181.871
0.020       0.000         2181.871       2181.871
0.010       0.000         2181.871       2181.871

Sample-Size Adjusted BIC (n* = (n + 2) / 24)

Mean                              2143.782
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000         2143.782       2143.782
0.980       0.000         2143.782       2143.782
0.950       0.000         2143.782       2143.782
0.900       0.000         2143.782       2143.782
0.800       0.000         2143.782       2143.782
0.700       0.000         2143.782       2143.782
0.500       0.000         2143.782       2143.782
0.300       0.000         2143.782       2143.782
0.200       0.000         2143.782       2143.782
0.100       0.000         2143.782       2143.782
0.050       0.000         2143.782       2143.782
0.020       0.000         2143.782       2143.782
0.010       0.000         2143.782       2143.782

MODEL RESULTS

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

IW       |
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
U3                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
U4                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000

SW       |
U1                  0.000     0.0000     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
U3                  2.000     2.0000     0.0000     0.0000     0.0000 1.000 0.000
U4                  3.000     3.0000     0.0000     0.0000     0.0000 1.000 0.000

IW         ON
X                   1.000     1.1054     0.0000     0.1320     0.0111 1.000 1.000

SW         ON
X                   0.200     0.1053     0.0000     0.0815     0.0090 1.000 0.000

SW       WITH
IW                  0.000     0.2347     0.0000     0.0940     0.0551 0.000 1.000

Residual Variances
IW                  1.000     0.4328     0.0000     0.2789     0.3218 0.000 0.000
SW                  0.500     0.1963     0.0000     0.1154     0.0922 0.000 0.000

Between Level

IB       |
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
U3                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
U4                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000

SB       |
U1                  0.000     0.0000     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
U3                  2.000     2.0000     0.0000     0.0000     0.0000 1.000 0.000
U4                  3.000     3.0000     0.0000     0.0000     0.0000 1.000 0.000

IB         ON
W                   0.500     0.3456     0.0000     0.1124     0.0238 1.000 1.000

SB         ON
W                   0.200     0.3195     0.0000     0.0926     0.0143 1.000 1.000

SB       WITH
IB                  0.000    -0.1940     0.0000     0.1223     0.0376 1.000 0.000

Intercepts
IB                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
SB                  0.500     0.3516     0.0000     0.0932     0.0220 1.000 1.000

Thresholds
U1\$1                0.000    -0.1330     0.0000     0.1292     0.0177 1.000 0.000
U2\$1                0.000    -0.1330     0.0000     0.1292     0.0177 1.000 0.000
U3\$1                0.000    -0.1330     0.0000     0.1292     0.0177 1.000 0.000
U4\$1                0.000    -0.1330     0.0000     0.1292     0.0177 1.000 0.000

Residual Variances
IB                  0.500     0.5119     0.0000     0.2311     0.0001 1.000 1.000
SB                  0.300     0.3171     0.0000     0.1198     0.0003 1.000 1.000

QUALITY OF NUMERICAL RESULTS

Average Condition Number for the Information Matrix      0.122E-02
(ratio of smallest to largest eigenvalue)

TECHNICAL 1 OUTPUT

PARAMETER SPECIFICATION FOR WITHIN

TAU
U1\$1          U2\$1          U3\$1          U4\$1
________      ________      ________      ________
0             0             0             0

NU
U1            U2            U3            U4            X
________      ________      ________      ________      ________
0             0             0             0             0

LAMBDA
IW            SW            X
________      ________      ________
U1                 0             0             0
U2                 0             0             0
U3                 0             0             0
U4                 0             0             0
X                  0             0             0

THETA
U1            U2            U3            U4            X
________      ________      ________      ________      ________
U1                 0
U2                 0             0
U3                 0             0             0
U4                 0             0             0             0
X                  0             0             0             0             0

ALPHA
IW            SW            X
________      ________      ________
0             0             0

BETA
IW            SW            X
________      ________      ________
IW                 0             0             1
SW                 0             0             2
X                  0             0             0

PSI
IW            SW            X
________      ________      ________
IW                 3
SW                 4             5
X                  0             0             0

PARAMETER SPECIFICATION FOR BETWEEN

TAU
U1\$1          U2\$1          U3\$1          U4\$1
________      ________      ________      ________
12            12            12            12

NU
U1            U2            U3            U4            W
________      ________      ________      ________      ________
0             0             0             0             0

LAMBDA
IB            SB            W
________      ________      ________
U1                 0             0             0
U2                 0             0             0
U3                 0             0             0
U4                 0             0             0
W                  0             0             0

THETA
U1            U2            U3            U4            W
________      ________      ________      ________      ________
U1                 0
U2                 0             0
U3                 0             0             0
U4                 0             0             0             0
W                  0             0             0             0             0

ALPHA
IB            SB            W
________      ________      ________
0             6             0

BETA
IB            SB            W
________      ________      ________
IB                 0             0             7
SB                 0             0             8
W                  0             0             0

PSI
IB            SB            W
________      ________      ________
IB                 9
SB                10            11
W                  0             0             0

STARTING VALUES FOR WITHIN

TAU
U1\$1          U2\$1          U3\$1          U4\$1
________      ________      ________      ________
0.000         0.000         0.000         0.000

NU
U1            U2            U3            U4            X
________      ________      ________      ________      ________
0.000         0.000         0.000         0.000         0.000

LAMBDA
IW            SW            X
________      ________      ________
U1             1.000         0.000         0.000
U2             1.000         1.000         0.000
U3             1.000         2.000         0.000
U4             1.000         3.000         0.000
X              0.000         0.000         1.000

THETA
U1            U2            U3            U4            X
________      ________      ________      ________      ________
U1             1.000
U2             0.000         1.000
U3             0.000         0.000         1.000
U4             0.000         0.000         0.000         1.000
X              0.000         0.000         0.000         0.000         0.000

ALPHA
IW            SW            X
________      ________      ________
0.000         0.000         0.000

BETA
IW            SW            X
________      ________      ________
IW             0.000         0.000         1.000
SW             0.000         0.000         0.200
X              0.000         0.000         0.000

PSI
IW            SW            X
________      ________      ________
IW             1.000
SW             0.000         0.500
X              0.000         0.000         0.500

STARTING VALUES FOR BETWEEN

TAU
U1\$1          U2\$1          U3\$1          U4\$1
________      ________      ________      ________
0.000         0.000         0.000         0.000

NU
U1            U2            U3            U4            W
________      ________      ________      ________      ________
0.000         0.000         0.000         0.000         0.000

LAMBDA
IB            SB            W
________      ________      ________
U1             1.000         0.000         0.000
U2             1.000         1.000         0.000
U3             1.000         2.000         0.000
U4             1.000         3.000         0.000
W              0.000         0.000         1.000

THETA
U1            U2            U3            U4            W
________      ________      ________      ________      ________
U1             0.000
U2             0.000         0.000
U3             0.000         0.000         0.000
U4             0.000         0.000         0.000         0.000
W              0.000         0.000         0.000         0.000         0.000

ALPHA
IB            SB            W
________      ________      ________
0.000         0.500         0.000

BETA
IB            SB            W
________      ________      ________
IB             0.000         0.000         0.500
SB             0.000         0.000         0.200
W              0.000         0.000         0.000

PSI
IB            SB            W
________      ________      ________
IB             0.500
SB             0.000         0.300
W              0.000         0.000         0.500

POPULATION VALUES FOR WITHIN

TAU
U1\$1          U2\$1          U3\$1          U4\$1
________      ________      ________      ________
0.000         0.000         0.000         0.000

NU
U1            U2            U3            U4            X
________      ________      ________      ________      ________
0.000         0.000         0.000         0.000         0.000

LAMBDA
IW            SW            X
________      ________      ________
U1             1.000         0.000         0.000
U2             1.000         1.000         0.000
U3             1.000         2.000         0.000
U4             1.000         3.000         0.000
X              0.000         0.000         1.000

THETA
U1            U2            U3            U4            X
________      ________      ________      ________      ________
U1             0.000
U2             0.000         0.000
U3             0.000         0.000         0.000
U4             0.000         0.000         0.000         0.000
X              0.000         0.000         0.000         0.000         0.000

ALPHA
IW            SW            X
________      ________      ________
0.000         0.000         0.000

BETA
IW            SW            X
________      ________      ________
IW             0.000         0.000         1.000
SW             0.000         0.000         0.200
X              0.000         0.000         0.000

PSI
IW            SW            X
________      ________      ________
IW             1.000
SW             0.000         0.500
X              0.000         0.000         1.000

POPULATION VALUES FOR BETWEEN

TAU
U1\$1          U2\$1          U3\$1          U4\$1
________      ________      ________      ________
0.000         0.000         0.000         0.000

NU
U1            U2            U3            U4            W
________      ________      ________      ________      ________
0.000         0.000         0.000         0.000         0.000

LAMBDA
IB            SB            W
________      ________      ________
U1             1.000         0.000         0.000
U2             1.000         1.000         0.000
U3             1.000         2.000         0.000
U4             1.000         3.000         0.000
W              0.000         0.000         1.000

THETA
U1            U2            U3            U4            W
________      ________      ________      ________      ________
U1             0.000
U2             0.000         0.000
U3             0.000         0.000         0.000
U4             0.000         0.000         0.000         0.000
W              0.000         0.000         0.000         0.000         0.000

ALPHA
IB            SB            W
________      ________      ________
0.000         0.500         0.000

BETA
IB            SB            W
________      ________      ________
IB             0.000         0.000         0.500
SB             0.000         0.000         0.200
W              0.000         0.000         0.000

PSI
IB            SB            W
________      ________      ________
IB             0.500
SB             0.000         0.300
W              0.000         0.000         1.000

TECHNICAL 8 OUTPUT

TECHNICAL 8 OUTPUT FOR REPLICATION 1

E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
1 -0.10608231D+04    0.0000000    0.0000000  EM
2 -0.10583263D+04    2.4968106    0.0023537  FS
3 -0.10556395D+04    2.6868343    0.0025388  EM
4 -0.10546308D+04    1.0086982    0.0009555  EM
5 -0.10541687D+04    0.4620405    0.0004381  EM
6 -0.10539441D+04    0.2246450    0.0002131  EM
7 -0.10538286D+04    0.1155033    0.0001096  EM
8 -0.10537657D+04    0.0628311    0.0000596  EM
9 -0.10537295D+04    0.0362450    0.0000344  EM
10 -0.10537073D+04    0.0222341    0.0000211  EM
11 -0.10536927D+04    0.0145187    0.0000138  EM
12 -0.10536827D+04    0.0100653    0.0000096  EM
13 -0.10536753D+04    0.0073586    0.0000070  EM
14 -0.10536697D+04    0.0056200    0.0000053  EM
15 -0.10536653D+04    0.0044387    0.0000042  EM
16 -0.10536617D+04    0.0035926    0.0000034  EM
17 -0.10536587D+04    0.0029583    0.0000028  EM
18 -0.10536562D+04    0.0024648    0.0000023  EM
19 -0.10536542D+04    0.0020700    0.0000020  EM
20 -0.10536524D+04    0.0017478    0.0000017  EM
21 -0.10536509D+04    0.0014812    0.0000014  EM
22 -0.10536497D+04    0.0012583    0.0000012  EM
23 -0.10536486D+04    0.0010708    0.0000010  EM
24 -0.10536477D+04    0.0009124    0.0000009  EM

TECHNICAL 9 OUTPUT

Error messages for each replication (if any)

SAVEDATA INFORMATION

Order of variables

U1
U2
U3
U4
X
W
CLUSTER

Save file
ex9.13.dat

Save file format           Free
Save file record length    10000

Beginning Time:  03:30:32
Ending Time:  03:30:52
Elapsed Time:  00:00:20

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