Mplus VERSION 7.2
MUTHEN & MUTHEN
05/07/2014   2:09 PM

INPUT INSTRUCTIONS

  TITLE:	Monte Carlo for a two-level path
  	analysis model with a continuous and a
  	categorical dependent variable

  montecarlo:
  	names are y1 u2 x1 x2 w;
  	generate = u2(1);
  	categorical = u2;
  	nobservations = 1000;
  	ncsizes = 3;
  	csizes = 40 (5) 50 (10) 20 (15);
  	seed = 58459;
  	nreps = 1;
  	within = x1 x2;
  	between = w;
  	save = ex9.3.dat;

  ANALYSIS:	
  	TYPE = TWOLEVEL;
  	algo = int;

  model population:

  	%WITHIN%

  	x1-x2@1;

  	u2 ON y1*.75 x2*.5;
  	y1 ON x1*.25 x2*.5;
  	y1*1;

  	%BETWEEN%

  	w@1;

  	u2 ON w*1;
  	y1 ON w*.5;
  	y1*.5; u2*.4;

  model:

  	%WITHIN%

  	u2 ON y1*.75 x2*.5;
  	y1 ON x1*.25 x2*.5;
  	y1*1;

  	%BETWEEN%

  	u2 ON w*1;
  	y1 ON w*.5;
  	y1*.5; u2*.4;


  output:
  	tech8 tech9;



INPUT READING TERMINATED NORMALLY



Monte Carlo for a two-level path
analysis model with a continuous and a
categorical dependent variable

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                        1000

Number of replications
    Requested                                                    1
    Completed                                                    1
Value of seed                                                58459

Number of dependent variables                                    2
Number of independent variables                                  3
Number of continuous latent variables                            0

Observed dependent variables

  Continuous
   Y1

  Binary and ordered categorical (ordinal)
   U2

Observed independent variables
   X1          X2          W

Variables with special functions

  Within variables
   X1          X2

  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                                  15
  Dimensions of numerical integration                            1
  Adaptive quadrature                                           ON
Link                                                         LOGIT
Cholesky                                                       OFF


SUMMARY OF DATA FOR THE FIRST REPLICATION

     Cluster information

       Size (s)    Number of clusters of Size s

          5            40
         10            50
         15            20


SAMPLE STATISTICS FOR THE FIRST REPLICATION


     SAMPLE STATISTICS


           Means
              Y1            X1            X2            W
              ________      ________      ________      ________
 1              0.155        -0.001         0.047         0.084


           Covariances
              Y1            X1            X2            W
              ________      ________      ________      ________
 Y1             2.019
 X1             0.223         1.039
 X2             0.409        -0.023         0.984
 W              0.589        -0.026        -0.003         1.067


           Correlations
              Y1            X1            X2            W
              ________      ________      ________      ________
 Y1             1.000
 X1             0.154         1.000
 X2             0.290        -0.023         1.000
 W              0.401        -0.025        -0.003         1.000




MODEL FIT INFORMATION

Number of Free Parameters                       11

Loglikelihood

    H0 Value

        Mean                             -1965.263
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        -1965.263      -1965.263
           0.980       0.000        -1965.263      -1965.263
           0.950       0.000        -1965.263      -1965.263
           0.900       0.000        -1965.263      -1965.263
           0.800       0.000        -1965.263      -1965.263
           0.700       0.000        -1965.263      -1965.263
           0.500       0.000        -1965.263      -1965.263
           0.300       0.000        -1965.263      -1965.263
           0.200       0.000        -1965.263      -1965.263
           0.100       0.000        -1965.263      -1965.263
           0.050       0.000        -1965.263      -1965.263
           0.020       0.000        -1965.263      -1965.263
           0.010       0.000        -1965.263      -1965.263

Information Criteria

    Akaike (AIC)

        Mean                              3952.526
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         3952.526       3952.526
           0.980       0.000         3952.526       3952.526
           0.950       0.000         3952.526       3952.526
           0.900       0.000         3952.526       3952.526
           0.800       0.000         3952.526       3952.526
           0.700       0.000         3952.526       3952.526
           0.500       0.000         3952.526       3952.526
           0.300       0.000         3952.526       3952.526
           0.200       0.000         3952.526       3952.526
           0.100       0.000         3952.526       3952.526
           0.050       0.000         3952.526       3952.526
           0.020       0.000         3952.526       3952.526
           0.010       0.000         3952.526       3952.526

    Bayesian (BIC)

        Mean                              4006.512
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         4006.512       4006.512
           0.980       0.000         4006.512       4006.512
           0.950       0.000         4006.512       4006.512
           0.900       0.000         4006.512       4006.512
           0.800       0.000         4006.512       4006.512
           0.700       0.000         4006.512       4006.512
           0.500       0.000         4006.512       4006.512
           0.300       0.000         4006.512       4006.512
           0.200       0.000         4006.512       4006.512
           0.100       0.000         4006.512       4006.512
           0.050       0.000         4006.512       4006.512
           0.020       0.000         4006.512       4006.512
           0.010       0.000         4006.512       4006.512

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

        Mean                              3971.575
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         3971.575       3971.575
           0.980       0.000         3971.575       3971.575
           0.950       0.000         3971.575       3971.575
           0.900       0.000         3971.575       3971.575
           0.800       0.000         3971.575       3971.575
           0.700       0.000         3971.575       3971.575
           0.500       0.000         3971.575       3971.575
           0.300       0.000         3971.575       3971.575
           0.200       0.000         3971.575       3971.575
           0.100       0.000         3971.575       3971.575
           0.050       0.000         3971.575       3971.575
           0.020       0.000         3971.575       3971.575
           0.010       0.000         3971.575       3971.575



MODEL RESULTS

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

 U2         ON
  Y1                  0.750     0.7453     0.0000     0.0850     0.0000 1.000 1.000
  X2                  0.500     0.5329     0.0000     0.1065     0.0011 1.000 1.000

 Y1         ON
  X1                  0.250     0.2287     0.0000     0.0344     0.0005 1.000 1.000
  X2                  0.500     0.4536     0.0000     0.0331     0.0021 1.000 1.000

 Residual Variances
  Y1                  1.000     1.0043     0.0000     0.0489     0.0000 1.000 1.000

Between Level

 U2         ON
  W                   1.000     1.2667     0.0000     0.1322     0.0711 0.000 1.000

 Y1         ON
  W                   0.500     0.5772     0.0000     0.0632     0.0060 1.000 1.000

 Intercepts
  Y1                  0.000     0.0963     0.0000     0.0733     0.0093 1.000 0.000

 Thresholds
  U2$1                0.000     0.0743     0.0000     0.1009     0.0055 1.000 0.000

 Residual Variances
  U2                  0.400     0.2672     0.0000     0.1400     0.0176 1.000 0.000
  Y1                  0.500     0.4552     0.0000     0.0690     0.0020 1.000 1.000


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.333E-01
       (ratio of smallest to largest eigenvalue)


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR WITHIN


           TAU
              U2$1
              ________
 1                  0


           NU
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 1                  0             0             0             0             0


           LAMBDA
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 U2                 0             0             0             0             0
 Y1                 0             0             0             0             0
 X1                 0             0             0             0             0
 X2                 0             0             0             0             0
 W                  0             0             0             0             0


           THETA
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 U2                 0
 Y1                 0             0
 X1                 0             0             0
 X2                 0             0             0             0
 W                  0             0             0             0             0


           ALPHA
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 1                  0             0             0             0             0


           BETA
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 U2                 0             1             0             2             0
 Y1                 0             0             3             4             0
 X1                 0             0             0             0             0
 X2                 0             0             0             0             0
 W                  0             0             0             0             0


           PSI
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 U2                 0
 Y1                 0             5
 X1                 0             0             0
 X2                 0             0             0             0
 W                  0             0             0             0             0


     PARAMETER SPECIFICATION FOR BETWEEN


           TAU
              U2$1
              ________
 1                 11


           NU
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 1                  0             0             0             0             0


           LAMBDA
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 U2                 0             0             0             0             0
 Y1                 0             0             0             0             0
 X1                 0             0             0             0             0
 X2                 0             0             0             0             0
 W                  0             0             0             0             0


           THETA
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 U2                 0
 Y1                 0             0
 X1                 0             0             0
 X2                 0             0             0             0
 W                  0             0             0             0             0


           ALPHA
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 1                  0             6             0             0             0


           BETA
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 U2                 0             0             0             0             7
 Y1                 0             0             0             0             8
 X1                 0             0             0             0             0
 X2                 0             0             0             0             0
 W                  0             0             0             0             0


           PSI
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 U2                 9
 Y1                 0            10
 X1                 0             0             0
 X2                 0             0             0             0
 W                  0             0             0             0             0


     STARTING VALUES FOR WITHIN


           TAU
              U2$1
              ________
 1              0.000


           NU
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           LAMBDA
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 U2             1.000         0.000         0.000         0.000         0.000
 Y1             0.000         1.000         0.000         0.000         0.000
 X1             0.000         0.000         1.000         0.000         0.000
 X2             0.000         0.000         0.000         1.000         0.000
 W              0.000         0.000         0.000         0.000         1.000


           THETA
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 U2             0.000
 Y1             0.000         0.000
 X1             0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000


           ALPHA
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           BETA
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 U2             0.000         0.750         0.000         0.500         0.000
 Y1             0.000         0.000         0.250         0.500         0.000
 X1             0.000         0.000         0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000


           PSI
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 U2             1.000
 Y1             0.000         1.000
 X1             0.000         0.000         0.500
 X2             0.000         0.000         0.000         0.500
 W              0.000         0.000         0.000         0.000         0.000


     STARTING VALUES FOR BETWEEN


           TAU
              U2$1
              ________
 1              0.000


           NU
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           LAMBDA
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 U2             1.000         0.000         0.000         0.000         0.000
 Y1             0.000         1.000         0.000         0.000         0.000
 X1             0.000         0.000         1.000         0.000         0.000
 X2             0.000         0.000         0.000         1.000         0.000
 W              0.000         0.000         0.000         0.000         1.000


           THETA
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 U2             0.000
 Y1             0.000         0.000
 X1             0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000


           ALPHA
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           BETA
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 U2             0.000         0.000         0.000         0.000         1.000
 Y1             0.000         0.000         0.000         0.000         0.500
 X1             0.000         0.000         0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000


           PSI
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 U2             0.400
 Y1             0.000         0.500
 X1             0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.500


     POPULATION VALUES FOR WITHIN


           TAU
              U2$1
              ________
 1              0.000


           NU
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           LAMBDA
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 U2             1.000         0.000         0.000         0.000         0.000
 Y1             0.000         1.000         0.000         0.000         0.000
 X1             0.000         0.000         1.000         0.000         0.000
 X2             0.000         0.000         0.000         1.000         0.000
 W              0.000         0.000         0.000         0.000         1.000


           THETA
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 U2             0.000
 Y1             0.000         0.000
 X1             0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000


           ALPHA
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           BETA
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 U2             0.000         0.750         0.000         0.500         0.000
 Y1             0.000         0.000         0.250         0.500         0.000
 X1             0.000         0.000         0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000


           PSI
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 U2             0.000
 Y1             0.000         1.000
 X1             0.000         0.000         1.000
 X2             0.000         0.000         0.000         1.000
 W              0.000         0.000         0.000         0.000         0.000


     POPULATION VALUES FOR BETWEEN


           TAU
              U2$1
              ________
 1              0.000


           NU
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           LAMBDA
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 U2             1.000         0.000         0.000         0.000         0.000
 Y1             0.000         1.000         0.000         0.000         0.000
 X1             0.000         0.000         1.000         0.000         0.000
 X2             0.000         0.000         0.000         1.000         0.000
 W              0.000         0.000         0.000         0.000         1.000


           THETA
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 U2             0.000
 Y1             0.000         0.000
 X1             0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000


           ALPHA
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           BETA
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 U2             0.000         0.000         0.000         0.000         1.000
 Y1             0.000         0.000         0.000         0.000         0.500
 X1             0.000         0.000         0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000


           PSI
              U2            Y1            X1            X2            W
              ________      ________      ________      ________      ________
 U2             0.400
 Y1             0.000         0.500
 X1             0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000
 W              0.000         0.000         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 -0.19710748D+04    0.0000000    0.0000000  EM
              2 -0.19671720D+04    3.9027486    0.0019800  EM
              3 -0.19664382D+04    0.7338421    0.0003730  EM
              4 -0.19660494D+04    0.3888077    0.0001977  EM
              5 -0.19658046D+04    0.2448273    0.0001245  EM
              6 -0.19656435D+04    0.1610463    0.0000819  EM
              7 -0.19655350D+04    0.1085165    0.0000552  EM
              8 -0.19654605D+04    0.0745013    0.0000379  EM
              9 -0.19654085D+04    0.0520189    0.0000265  EM
             10 -0.19653716D+04    0.0368916    0.0000188  EM
             11 -0.19653450D+04    0.0265550    0.0000135  EM
             12 -0.19653256D+04    0.0193917    0.0000099  EM
             13 -0.19653113D+04    0.0143615    0.0000073  EM
             14 -0.19653005D+04    0.0107844    0.0000055  EM
             15 -0.19652923D+04    0.0082088    0.0000042  EM
             16 -0.19652860D+04    0.0063319    0.0000032  EM
             17 -0.19652810D+04    0.0049476    0.0000025  EM
             18 -0.19652771D+04    0.0039142    0.0000020  EM
             19 -0.19652740D+04    0.0031334    0.0000016  EM
             20 -0.19652714D+04    0.0025363    0.0000013  EM
             21 -0.19652694D+04    0.0020742    0.0000011  EM
             22 -0.19652676D+04    0.0017125    0.0000009  EM
             23 -0.19652662D+04    0.0014260    0.0000007  EM
             24 -0.19652650D+04    0.0011966    0.0000006  EM
             25 -0.19652640D+04    0.0010111    0.0000005  EM
             26 -0.19652631D+04    0.0008595    0.0000004  EM


TECHNICAL 9 OUTPUT

  Error messages for each replication (if any)



SAVEDATA INFORMATION

  Order of variables

    U2
    Y1
    X1
    X2
    W
    CLUSTER

  Save file
    ex9.3.dat

  Save file format           Free
  Save file record length    10000


     Beginning Time:  14:09:03
        Ending Time:  14:09:03
       Elapsed Time:  00:00:00



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