Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022  11:20 PM

INPUT INSTRUCTIONS

  TITLE:	this is an example of a two-level
  growth model for a count outcome using a
  zero-inflated Poisson model (three-level analysis)
  DATA:	FILE = ex9.17.dat;
  VARIABLE:	NAMES = u1-u4 x w clus;
  	COUNT = u1-u4 (i);
  	CLUSTER = clus;
  	WITHIN = x;
  	BETWEEN = w;
  ANALYSIS:	TYPE = TWOLEVEL;
  	ALGORITHM = INTEGRATION;
  	INTEGRATION = 10;
  	MCONVERGENCE = 0.01;
  MODEL:	%WITHIN%
  	iw sw | u1@0 u2@1 u3@2 u4@3;
  	iiw siw | u1#1@0 u2#1@1 u3#1@2 u4#1@3;
  	sw@0;
  	siw@0;
  	iw WITH iiw;
  	iw ON x;
  	sw ON x;
  	%BETWEEN%
  	ib sb | u1@0 u2@1 u3@2 u4@3;
  	iib sib | u1#1@0 u2#1@1 u3#1@2 u4#1@3;
  	sb-sib@0;
  	ib ON w;
  OUTPUT:	TECH1 TECH8;



*** WARNING
  One or more individual-level variables have no variation within a
  cluster for the following clusters.

     Variable   Cluster IDs with no within-cluster variation

      U1          11 22 65
      U2          20 78
      U3          11 13
      U4          74

*** WARNING in MODEL command
  All continuous latent variable covariances involving SB on the between level
  have been fixed to 0 because the variance of SB is fixed at 0.
*** WARNING in MODEL command
  All continuous latent variable covariances involving IIB on the between level
  have been fixed to 0 because the variance of IIB is fixed at 0.
*** WARNING in MODEL command
  All continuous latent variable covariances involving SW on the within level
  have been fixed to 0 because the variance of SW is fixed at 0.
*** WARNING in MODEL command
  All continuous latent variable covariances involving SIW on the within level
  have been fixed to 0 because the variance of SIW is fixed at 0.
   5 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS



this is an example of a two-level
growth model for a count outcome using a
zero-inflated Poisson model (three-level analysis)

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                        1000

Number of dependent variables                                    4
Number of independent variables                                  2
Number of continuous latent variables                            8

Observed dependent variables

  Count
   U1          U2          U3          U4

Observed independent variables
   X           W

Continuous latent variables
   IW          SW          IIW         SIW         IB          SB
   IIB         SIB

Variables with special functions

  Cluster variable      CLUS

  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-01
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                                  10
  Dimensions of numerical integration                            3
  Adaptive quadrature                                           ON
Cholesky                                                        ON

Input data file(s)
  ex9.17.dat
Input data format  FREE


SUMMARY OF DATA

     Number of clusters                        110



COUNT PROPORTION OF ZERO, MINIMUM AND MAXIMUM VALUES

      U1          0.583         0        25
      U2          0.552         0        17
      U3          0.544         0        24
      U4          0.494         0        33



UNIVARIATE SAMPLE STATISTICS


     UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS

         Variable/         Mean/     Skewness/   Minimum/ % with                Percentiles
        Sample Size      Variance    Kurtosis    Maximum  Min/Max      20%/60%    40%/80%    Median

     X                     0.012      -0.061      -2.915    0.10%      -0.847     -0.221      0.035
            1000.000       1.035       0.012       2.908    0.10%       0.261      0.847
     W                    -0.110       0.297      -2.356    0.91%      -1.094     -0.386     -0.116
             110.000       1.003      -0.088       3.033    0.91%       0.152      0.752


THE MODEL ESTIMATION TERMINATED NORMALLY



MODEL FIT INFORMATION

Number of Free Parameters                       11

Loglikelihood

          H0 Value                       -5512.265
          H0 Scaling Correction Factor      0.9910
            for MLR

Information Criteria

          Akaike (AIC)                   11046.531
          Bayesian (BIC)                 11100.516
          Sample-Size Adjusted BIC       11065.579
            (n* = (n + 2) / 24)



MODEL RESULTS

                                                    Two-Tailed
                    Estimate       S.E.  Est./S.E.    P-Value

Within Level

 IW       |
    U1                 1.000      0.000    999.000    999.000
    U2                 1.000      0.000    999.000    999.000
    U3                 1.000      0.000    999.000    999.000
    U4                 1.000      0.000    999.000    999.000

 SW       |
    U1                 0.000      0.000    999.000    999.000
    U2                 1.000      0.000    999.000    999.000
    U3                 2.000      0.000    999.000    999.000
    U4                 3.000      0.000    999.000    999.000

 IIW      |
    U1#1               1.000      0.000    999.000    999.000
    U2#1               1.000      0.000    999.000    999.000
    U3#1               1.000      0.000    999.000    999.000
    U4#1               1.000      0.000    999.000    999.000

 SIW      |
    U1#1               0.000      0.000    999.000    999.000
    U2#1               1.000      0.000    999.000    999.000
    U3#1               2.000      0.000    999.000    999.000
    U4#1               3.000      0.000    999.000    999.000

 IW         ON
    X                  0.167      0.041      4.083      0.000

 SW         ON
    X                  0.046      0.014      3.249      0.001

 IW       WITH
    IIW               -0.281      0.068     -4.160      0.000

 Variances
    IIW                0.783      0.274      2.862      0.004
    SIW                0.000      0.000    999.000    999.000

 Residual Variances
    IW                 0.438      0.041     10.668      0.000
    SW                 0.000      0.000    999.000    999.000

Between Level

 IB       |
    U1                 1.000      0.000    999.000    999.000
    U2                 1.000      0.000    999.000    999.000
    U3                 1.000      0.000    999.000    999.000
    U4                 1.000      0.000    999.000    999.000

 SB       |
    U1                 0.000      0.000    999.000    999.000
    U2                 1.000      0.000    999.000    999.000
    U3                 2.000      0.000    999.000    999.000
    U4                 3.000      0.000    999.000    999.000

 IIB      |
    U1#1               1.000      0.000    999.000    999.000
    U2#1               1.000      0.000    999.000    999.000
    U3#1               1.000      0.000    999.000    999.000
    U4#1               1.000      0.000    999.000    999.000

 SIB      |
    U1#1               0.000      0.000    999.000    999.000
    U2#1               1.000      0.000    999.000    999.000
    U3#1               2.000      0.000    999.000    999.000
    U4#1               3.000      0.000    999.000    999.000

 IB         ON
    W                  0.441      0.046      9.563      0.000

 Means
    SB                 0.016      0.015      1.068      0.286
    IIB                0.000      0.000    999.000    999.000
    SIB               -0.209      0.050     -4.135      0.000

 Intercepts
    IB                 0.188      0.063      2.991      0.003
    U1#1              -0.522      0.109     -4.781      0.000
    U1                 0.000      0.000    999.000    999.000
    U2#1              -0.522      0.109     -4.781      0.000
    U2                 0.000      0.000    999.000    999.000
    U3#1              -0.522      0.109     -4.781      0.000
    U3                 0.000      0.000    999.000    999.000
    U4#1              -0.522      0.109     -4.781      0.000
    U4                 0.000      0.000    999.000    999.000

 Variances
    SB                 0.000      0.000    999.000    999.000
    IIB                0.000      0.000    999.000    999.000
    SIB                0.000      0.000    999.000    999.000

 Residual Variances
    IB                 0.181      0.044      4.141      0.000


QUALITY OF NUMERICAL RESULTS

     Condition Number for the Information Matrix              0.174E-02
       (ratio of smallest to largest eigenvalue)


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR WITHIN


           NU
              U1#1          U1            U2#1          U2            U3#1
              ________      ________      ________      ________      ________
                    0             0             0             0             0


           NU
              U3            U4#1          U4            X
              ________      ________      ________      ________
                    0             0             0             0


           LAMBDA
              IW            SW            IIW           SIW           X
              ________      ________      ________      ________      ________
 U1#1               0             0             0             0             0
 U1                 0             0             0             0             0
 U2#1               0             0             0             0             0
 U2                 0             0             0             0             0
 U3#1               0             0             0             0             0
 U3                 0             0             0             0             0
 U4#1               0             0             0             0             0
 U4                 0             0             0             0             0
 X                  0             0             0             0             0


           THETA
              U1#1          U1            U2#1          U2            U3#1
              ________      ________      ________      ________      ________
 U1#1               0
 U1                 0             0
 U2#1               0             0             0
 U2                 0             0             0             0
 U3#1               0             0             0             0             0
 U3                 0             0             0             0             0
 U4#1               0             0             0             0             0
 U4                 0             0             0             0             0
 X                  0             0             0             0             0


           THETA
              U3            U4#1          U4            X
              ________      ________      ________      ________
 U3                 0
 U4#1               0             0
 U4                 0             0             0
 X                  0             0             0             0


           ALPHA
              IW            SW            IIW           SIW           X
              ________      ________      ________      ________      ________
                    0             0             0             0             0


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


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


     PARAMETER SPECIFICATION FOR BETWEEN


           NU
              U1#1          U1            U2#1          U2            U3#1
              ________      ________      ________      ________      ________
                    6             0             6             0             6


           NU
              U3            U4#1          U4            W
              ________      ________      ________      ________
                    0             6             0             0


           LAMBDA
              IB            SB            IIB           SIB           W
              ________      ________      ________      ________      ________
 U1#1               0             0             0             0             0
 U1                 0             0             0             0             0
 U2#1               0             0             0             0             0
 U2                 0             0             0             0             0
 U3#1               0             0             0             0             0
 U3                 0             0             0             0             0
 U4#1               0             0             0             0             0
 U4                 0             0             0             0             0
 W                  0             0             0             0             0


           THETA
              U1#1          U1            U2#1          U2            U3#1
              ________      ________      ________      ________      ________
 U1#1               0
 U1                 0             0
 U2#1               0             0             0
 U2                 0             0             0             0
 U3#1               0             0             0             0             0
 U3                 0             0             0             0             0
 U4#1               0             0             0             0             0
 U4                 0             0             0             0             0
 W                  0             0             0             0             0


           THETA
              U3            U4#1          U4            W
              ________      ________      ________      ________
 U3                 0
 U4#1               0             0
 U4                 0             0             0
 W                  0             0             0             0


           ALPHA
              IB            SB            IIB           SIB           W
              ________      ________      ________      ________      ________
                    7             8             0             9             0


           BETA
              IB            SB            IIB           SIB           W
              ________      ________      ________      ________      ________
 IB                 0             0             0             0            10
 SB                 0             0             0             0             0
 IIB                0             0             0             0             0
 SIB                0             0             0             0             0
 W                  0             0             0             0             0


           PSI
              IB            SB            IIB           SIB           W
              ________      ________      ________      ________      ________
 IB                11
 SB                 0             0
 IIB                0             0             0
 SIB                0             0             0             0
 W                  0             0             0             0             0


     STARTING VALUES FOR WITHIN


           NU
              U1#1          U1            U2#1          U2            U3#1
              ________      ________      ________      ________      ________
                0.000         0.000         0.000         0.000         0.000


           NU
              U3            U4#1          U4            X
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           LAMBDA
              IW            SW            IIW           SIW           X
              ________      ________      ________      ________      ________
 U1#1           0.000         0.000         1.000         0.000         0.000
 U1             1.000         0.000         0.000         0.000         0.000
 U2#1           0.000         0.000         1.000         1.000         0.000
 U2             1.000         1.000         0.000         0.000         0.000
 U3#1           0.000         0.000         1.000         2.000         0.000
 U3             1.000         2.000         0.000         0.000         0.000
 U4#1           0.000         0.000         1.000         3.000         0.000
 U4             1.000         3.000         0.000         0.000         0.000
 X              0.000         0.000         0.000         0.000         1.000


           THETA
              U1#1          U1            U2#1          U2            U3#1
              ________      ________      ________      ________      ________
 U1#1           0.000
 U1             0.000         0.000
 U2#1           0.000         0.000         0.000
 U2             0.000         0.000         0.000         0.000
 U3#1           0.000         0.000         0.000         0.000         0.000
 U3             0.000         0.000         0.000         0.000         0.000
 U4#1           0.000         0.000         0.000         0.000         0.000
 U4             0.000         0.000         0.000         0.000         0.000
 X              0.000         0.000         0.000         0.000         0.000


           THETA
              U3            U4#1          U4            X
              ________      ________      ________      ________
 U3             0.000
 U4#1           0.000         0.000
 U4             0.000         0.000         0.000
 X              0.000         0.000         0.000         0.000


           ALPHA
              IW            SW            IIW           SIW           X
              ________      ________      ________      ________      ________
                0.000         0.000         0.000         0.000         0.000


           BETA
              IW            SW            IIW           SIW           X
              ________      ________      ________      ________      ________
 IW             0.000         0.000         0.000         0.000         0.000
 SW             0.000         0.000         0.000         0.000         0.000
 IIW            0.000         0.000         0.000         0.000         0.000
 SIW            0.000         0.000         0.000         0.000         0.000
 X              0.000         0.000         0.000         0.000         0.000


           PSI
              IW            SW            IIW           SIW           X
              ________      ________      ________      ________      ________
 IW             0.050
 SW             0.000         0.000
 IIW            0.000         0.000         0.050
 SIW            0.000         0.000         0.000         0.000
 X              0.000         0.000         0.000         0.000         0.518


     STARTING VALUES FOR BETWEEN


           NU
              U1#1          U1            U2#1          U2            U3#1
              ________      ________      ________      ________      ________
               -0.354         0.000        -0.354         0.000        -0.354


           NU
              U3            U4#1          U4            W
              ________      ________      ________      ________
                0.000        -0.354         0.000         0.000


           LAMBDA
              IB            SB            IIB           SIB           W
              ________      ________      ________      ________      ________
 U1#1           0.000         0.000         1.000         0.000         0.000
 U1             1.000         0.000         0.000         0.000         0.000
 U2#1           0.000         0.000         1.000         1.000         0.000
 U2             1.000         1.000         0.000         0.000         0.000
 U3#1           0.000         0.000         1.000         2.000         0.000
 U3             1.000         2.000         0.000         0.000         0.000
 U4#1           0.000         0.000         1.000         3.000         0.000
 U4             1.000         3.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         1.000


           THETA
              U1#1          U1            U2#1          U2            U3#1
              ________      ________      ________      ________      ________
 U1#1           0.000
 U1             0.000         0.000
 U2#1           0.000         0.000         0.000
 U2             0.000         0.000         0.000         0.000
 U3#1           0.000         0.000         0.000         0.000         0.000
 U3             0.000         0.000         0.000         0.000         0.000
 U4#1           0.000         0.000         0.000         0.000         0.000
 U4             0.000         0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000


           THETA
              U3            U4#1          U4            W
              ________      ________      ________      ________
 U3             0.000
 U4#1           0.000         0.000
 U4             0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000


           ALPHA
              IB            SB            IIB           SIB           W
              ________      ________      ________      ________      ________
                0.000         0.000         0.000         0.000         0.000


           BETA
              IB            SB            IIB           SIB           W
              ________      ________      ________      ________      ________
 IB             0.000         0.000         0.000         0.000         0.000
 SB             0.000         0.000         0.000         0.000         0.000
 IIB            0.000         0.000         0.000         0.000         0.000
 SIB            0.000         0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000


           PSI
              IB            SB            IIB           SIB           W
              ________      ________      ________      ________      ________
 IB             0.050
 SB             0.000         0.000
 IIB            0.000         0.000         0.000
 SIB            0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.478


TECHNICAL 8 OUTPUT


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.62459958D+04    0.0000000    0.0000000  EM
              2 -0.61490221D+04   96.9737596    0.0155257  FS
              3 -0.60954293D+04   53.5928014    0.0087157  FS
              4 -0.60496842D+04   45.7451056    0.0075048  FS
              5 -0.60078607D+04   41.8235011    0.0069133  FS
              6 -0.59695758D+04   38.2848216    0.0063725  FS
              7 -0.59343714D+04   35.2044842    0.0058973  FS
              8 -0.59017424D+04   32.6289823    0.0054983  FS
              9 -0.58704788D+04   31.2635535    0.0052973  FS
             10 -0.58492598D+04   21.2190464    0.0036145  FS
             11 -0.58151082D+04   34.1516191    0.0058386  FS
             12 -0.57863486D+04   28.7595440    0.0049457  FS
             13 -0.57572898D+04   29.0588229    0.0050220  FS
             14 -0.57278433D+04   29.4465248    0.0051147  FS
             15 -0.57008445D+04   26.9987530    0.0047136  FS
             16 -0.56035657D+04   97.2788098    0.0170639  EM
             17 -0.55797739D+04   23.7917520    0.0042458  FS
             18 -0.55613185D+04   18.4554432    0.0033076  FS
             19 -0.55471691D+04   14.1493962    0.0025443  FS
             20 -0.55364685D+04   10.7006281    0.0019290  FS
             21 -0.55284279D+04    8.0405697    0.0014523  FS
             22 -0.55224380D+04    5.9899284    0.0010835  FS
             23 -0.55180572D+04    4.3807806    0.0007933  FS
             24 -0.55150945D+04    2.9627472    0.0005369  FS
             25 -0.55133920D+04    1.7024759    0.0003087  FS
             26 -0.55126106D+04    0.7814194    0.0001417  FS
             27 -0.55123321D+04    0.2784264    0.0000505  FS
             28 -0.55122590D+04    0.0730898    0.0000133  FS
             29 -0.55122507D+04    0.0083427    0.0000015  FS
             30 -0.55122653D+04   -0.0145646   -0.0000026  EM


     Beginning Time:  23:20:18
        Ending Time:  23:20:36
       Elapsed Time:  00:00:18



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) 1998-2022 Muthen & Muthen

Back to examples