Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022  10:25 PM

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;



INPUT READING TERMINATED NORMALLY



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
  Adaptive quadrature                                           ON
Link                                                         LOGIT
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:  22:25:45
        Ending Time:  22:26:02
       Elapsed Time:  00:00:17



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