Mplus VERSION 7.2
MUTHEN & MUTHEN
05/07/2014   2:04 PM

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
  Adaptive quadrature                                           ON
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                  1             0             1             0             1


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


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


           NU
              U13           U14#1         U14
              ________      ________      ________
 1              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
              ________      ________      ________      ________
 1              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:  14:04:56
        Ending Time:  14:04:56
       Elapsed Time:  00:00:00



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