```Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   3:29 AM

INPUT INSTRUCTIONS

title:	this is an example of a linear growth
model for a count outcome using a zero-
inflated Poisson model

montecarlo:
names = u11-u14;
generate = u11-u14(ci);
count = u11-u14(i);
nobs = 500;
nreps = 1;
save = ex6.7.dat;

analysis:
integration = 7;

model population:

i s | u11@0 u12@1 u13@2 u14@3;
[u11-u14@0];

[i*.2 s*.005];
i*.4; s@0;

ii si | u11#1@0 u12#1@1 u13#1@2 u14#1@3;
[u11#1-u14#1*-.5];

[ii@0 si*-.2];
ii*1; si@0;
! inflation slope variance zero for simplicity
si with i-ii@0;
i with ii*-.32;
! correlation is -0.5 between i and ii
s with ii@0;

model:

i s | u11@0 u12@1 u13@2 u14@3;
[u11-u14@0];

[i*.2 s*.005];
i*.4; s@0;

ii si | u11#1@0 u12#1@1 u13#1@2 u14#1@3;
[u11#1-u14#1*-.5] (1);

[ii@0 si*-.2];
ii*1; si@0;

si with i-ii@0;
i with ii*-.32;
s with ii@0;

output:
tech8 tech9;

*** WARNING in MODEL command
All continuous latent variable covariances involving S have been fixed to 0
because the variance of S is fixed at 0.
1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS

this is an example of a linear growth
model for a count outcome using a zero-
inflated Poisson model

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                            4

Observed dependent variables

Count
U11         U12         U13         U14

Continuous latent variables
I           S           II          SI

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                            2
Cholesky                                                        ON

MODEL FIT INFORMATION

Number of Free Parameters                        7

Loglikelihood

H0 Value

Mean                             -2778.140
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000        -2778.140      -2778.140
0.980       0.000        -2778.140      -2778.140
0.950       0.000        -2778.140      -2778.140
0.900       0.000        -2778.140      -2778.140
0.800       0.000        -2778.140      -2778.140
0.700       0.000        -2778.140      -2778.140
0.500       0.000        -2778.140      -2778.140
0.300       0.000        -2778.140      -2778.140
0.200       0.000        -2778.140      -2778.140
0.100       0.000        -2778.140      -2778.140
0.050       0.000        -2778.140      -2778.140
0.020       0.000        -2778.140      -2778.140
0.010       0.000        -2778.140      -2778.140

Information Criteria

Akaike (AIC)

Mean                              5570.281
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000         5570.281       5570.281
0.980       0.000         5570.281       5570.281
0.950       0.000         5570.281       5570.281
0.900       0.000         5570.281       5570.281
0.800       0.000         5570.281       5570.281
0.700       0.000         5570.281       5570.281
0.500       0.000         5570.281       5570.281
0.300       0.000         5570.281       5570.281
0.200       0.000         5570.281       5570.281
0.100       0.000         5570.281       5570.281
0.050       0.000         5570.281       5570.281
0.020       0.000         5570.281       5570.281
0.010       0.000         5570.281       5570.281

Bayesian (BIC)

Mean                              5599.783
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000         5599.783       5599.783
0.980       0.000         5599.783       5599.783
0.950       0.000         5599.783       5599.783
0.900       0.000         5599.783       5599.783
0.800       0.000         5599.783       5599.783
0.700       0.000         5599.783       5599.783
0.500       0.000         5599.783       5599.783
0.300       0.000         5599.783       5599.783
0.200       0.000         5599.783       5599.783
0.100       0.000         5599.783       5599.783
0.050       0.000         5599.783       5599.783
0.020       0.000         5599.783       5599.783
0.010       0.000         5599.783       5599.783

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

Mean                              5577.565
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000         5577.565       5577.565
0.980       0.000         5577.565       5577.565
0.950       0.000         5577.565       5577.565
0.900       0.000         5577.565       5577.565
0.800       0.000         5577.565       5577.565
0.700       0.000         5577.565       5577.565
0.500       0.000         5577.565       5577.565
0.300       0.000         5577.565       5577.565
0.200       0.000         5577.565       5577.565
0.100       0.000         5577.565       5577.565
0.050       0.000         5577.565       5577.565
0.020       0.000         5577.565       5577.565
0.010       0.000         5577.565       5577.565

Chi-Square Test of Model Fit for the Count Outcomes

Pearson Chi-Square

Mean                              1915.459
Std Dev                              0.000
Degrees of freedom                    9973
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000         9647.393       1915.459
0.980       0.000         9685.098       1915.459
0.950       0.000         9741.839       1915.459
0.900       0.000         9792.440       1915.459
0.800       0.000         9853.947       1915.459
0.700       0.000         9898.458       1915.459
0.500       0.000         9972.333       1915.459
0.300       0.000        10046.575       1915.459
0.200       0.000        10091.664       1915.459
0.100       0.000        10154.417       1915.459
0.050       0.000        10206.435       1915.459
0.020       0.000        10265.192       1915.459
0.010       0.000        10304.489       1915.459

Likelihood Ratio Chi-Square

Mean                               652.622
Std Dev                              0.000
Degrees of freedom                    9973
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000         9647.393        652.622
0.980       0.000         9685.098        652.622
0.950       0.000         9741.839        652.622
0.900       0.000         9792.440        652.622
0.800       0.000         9853.947        652.622
0.700       0.000         9898.458        652.622
0.500       0.000         9972.333        652.622
0.300       0.000        10046.575        652.622
0.200       0.000        10091.664        652.622
0.100       0.000        10154.417        652.622
0.050       0.000        10206.435        652.622
0.020       0.000        10265.192        652.622
0.010       0.000        10304.489        652.622

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

II       |
U11#1               1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
U12#1               1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
U13#1               1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
U14#1               1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000

SI       |
U11#1               0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
U12#1               1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
U13#1               2.000     2.0000     0.0000     0.0000     0.0000 1.000 0.000
U14#1               3.000     3.0000     0.0000     0.0000     0.0000 1.000 0.000

SI       WITH
I                   0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
S                   0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
II                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

I        WITH
II                 -0.320    -0.2037     0.0000     0.1169     0.0135 1.000 0.000

S        WITH
II                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

Means
I                   0.200     0.3457     0.0000     0.0685     0.0212 0.000 1.000
S                   0.005    -0.0480     0.0000     0.0239     0.0028 0.000 1.000
II                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
SI                 -0.200    -0.4833     0.0000     0.0932     0.0802 0.000 1.000

Intercepts
U11#1              -0.500    -0.1614     0.0000     0.1487     0.1146 0.000 0.000
U11                 0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
U12#1              -0.500    -0.1614     0.0000     0.1487     0.1146 0.000 0.000
U12                 0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
U13#1              -0.500    -0.1614     0.0000     0.1487     0.1146 0.000 0.000
U13                 0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
U14#1              -0.500    -0.1614     0.0000     0.1487     0.1146 0.000 0.000
U14                 0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

Variances
I                   0.400     0.3858     0.0000     0.0595     0.0002 1.000 1.000
S                   0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
II                  1.000     1.1823     0.0000     0.5337     0.0332 1.000 1.000
SI                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

QUALITY OF NUMERICAL RESULTS

Average Condition Number for the Information Matrix      0.251E-02
(ratio of smallest to largest eigenvalue)

TECHNICAL 1 OUTPUT

PARAMETER SPECIFICATION

NU
U11#1         U11           U12#1         U12           U13#1
________      ________      ________      ________      ________
1             0             1             0             1

NU
U13           U14#1         U14
________      ________      ________
0             1             0

LAMBDA
I             S             II            SI
________      ________      ________      ________
U11#1              0             0             0             0
U11                0             0             0             0
U12#1              0             0             0             0
U12                0             0             0             0
U13#1              0             0             0             0
U13                0             0             0             0
U14#1              0             0             0             0
U14                0             0             0             0

THETA
U11#1         U11           U12#1         U12           U13#1
________      ________      ________      ________      ________
U11#1              0
U11                0             0
U12#1              0             0             0
U12                0             0             0             0
U13#1              0             0             0             0             0
U13                0             0             0             0             0
U14#1              0             0             0             0             0
U14                0             0             0             0             0

THETA
U13           U14#1         U14
________      ________      ________
U13                0
U14#1              0             0
U14                0             0             0

ALPHA
I             S             II            SI
________      ________      ________      ________
2             3             0             4

BETA
I             S             II            SI
________      ________      ________      ________
I                  0             0             0             0
S                  0             0             0             0
II                 0             0             0             0
SI                 0             0             0             0

PSI
I             S             II            SI
________      ________      ________      ________
I                  5
S                  0             0
II                 6             0             7
SI                 0             0             0             0

STARTING VALUES

NU
U11#1         U11           U12#1         U12           U13#1
________      ________      ________      ________      ________
-0.500         0.000        -0.500         0.000        -0.500

NU
U13           U14#1         U14
________      ________      ________
0.000        -0.500         0.000

LAMBDA
I             S             II            SI
________      ________      ________      ________
U11#1          0.000         0.000         1.000         0.000
U11            1.000         0.000         0.000         0.000
U12#1          0.000         0.000         1.000         1.000
U12            1.000         1.000         0.000         0.000
U13#1          0.000         0.000         1.000         2.000
U13            1.000         2.000         0.000         0.000
U14#1          0.000         0.000         1.000         3.000
U14            1.000         3.000         0.000         0.000

THETA
U11#1         U11           U12#1         U12           U13#1
________      ________      ________      ________      ________
U11#1          0.000
U11            0.000         0.000
U12#1          0.000         0.000         0.000
U12            0.000         0.000         0.000         0.000
U13#1          0.000         0.000         0.000         0.000         0.000
U13            0.000         0.000         0.000         0.000         0.000
U14#1          0.000         0.000         0.000         0.000         0.000
U14            0.000         0.000         0.000         0.000         0.000

THETA
U13           U14#1         U14
________      ________      ________
U13            0.000
U14#1          0.000         0.000
U14            0.000         0.000         0.000

ALPHA
I             S             II            SI
________      ________      ________      ________
0.200         0.005         0.000        -0.200

BETA
I             S             II            SI
________      ________      ________      ________
I              0.000         0.000         0.000         0.000
S              0.000         0.000         0.000         0.000
II             0.000         0.000         0.000         0.000
SI             0.000         0.000         0.000         0.000

PSI
I             S             II            SI
________      ________      ________      ________
I              0.400
S              0.000         0.000
II            -0.320         0.000         1.000
SI             0.000         0.000         0.000         0.000

POPULATION VALUES

NU
U11#1         U11           U12#1         U12           U13#1
________      ________      ________      ________      ________
-0.500         0.000        -0.500         0.000        -0.500

NU
U13           U14#1         U14
________      ________      ________
0.000        -0.500         0.000

LAMBDA
I             S             II            SI
________      ________      ________      ________
U11#1          0.000         0.000         1.000         0.000
U11            1.000         0.000         0.000         0.000
U12#1          0.000         0.000         1.000         1.000
U12            1.000         1.000         0.000         0.000
U13#1          0.000         0.000         1.000         2.000
U13            1.000         2.000         0.000         0.000
U14#1          0.000         0.000         1.000         3.000
U14            1.000         3.000         0.000         0.000

THETA
U11#1         U11           U12#1         U12           U13#1
________      ________      ________      ________      ________
U11#1          0.000
U11            0.000         0.000
U12#1          0.000         0.000         0.000
U12            0.000         0.000         0.000         0.000
U13#1          0.000         0.000         0.000         0.000         0.000
U13            0.000         0.000         0.000         0.000         0.000
U14#1          0.000         0.000         0.000         0.000         0.000
U14            0.000         0.000         0.000         0.000         0.000

THETA
U13           U14#1         U14
________      ________      ________
U13            0.000
U14#1          0.000         0.000
U14            0.000         0.000         0.000

ALPHA
I             S             II            SI
________      ________      ________      ________
0.200         0.005         0.000        -0.200

BETA
I             S             II            SI
________      ________      ________      ________
I              0.000         0.000         0.000         0.000
S              0.000         0.000         0.000         0.000
II             0.000         0.000         0.000         0.000
SI             0.000         0.000         0.000         0.000

PSI
I             S             II            SI
________      ________      ________      ________
I              0.400
S              0.000         0.000
II            -0.320         0.000         1.000
SI             0.000         0.000         0.000         0.000

TECHNICAL 8 OUTPUT

TECHNICAL 8 OUTPUT FOR REPLICATION 1

E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
1 -0.27881701D+04    0.0000000    0.0000000  EM
2 -0.27786996D+04    9.4705755    0.0033967  FS
3 -0.27781797D+04    0.5198755    0.0001871  FS
4 -0.27781473D+04    0.0324439    0.0000117  FS
5 -0.27781411D+04    0.0061493    0.0000022  FS
6 -0.27781404D+04    0.0006919    0.0000002  FS

TECHNICAL 9 OUTPUT

Error messages for each replication (if any)

SAVEDATA INFORMATION

Order of variables

U11
U12
U13
U14

Save file
ex6.7.dat

Save file format           Free
Save file record length    10000

Beginning Time:  03:29:19
Ending Time:  03:29:19
Elapsed Time:  00:00:00

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