Mplus VERSION 7
MUTHEN & MUTHEN
09/22/2012  10:08 PM

INPUT INSTRUCTIONS

  TITLE:	this is an example of a two-level
  		regression analysis for a continuous
  		dependent variable

  montecarlo:
  		names are y x w;
  		nobservations = 1000;
  		ncsizes = 3;
  		csizes = 40 (5) 50 (10) 20 (15);
  		seed = 58459;
  		nreps = 1;
  !		within = x;
          between = w;
  		save = ex9.1b.dat;

  ANALYSIS:  TYPE = TWOLEVEL;

  model population:
  		%within%
  		x@1;
  		y on x*.75;
  		y*1;
  		%between%
          [w@0]; w@1;
  		[x@0]; x@.5;
          w with x@.5;
  		y on w*.5 x*1;
  		[y*2];
  		y*.5;
  		
  model:
          %within%
  	
  		y on x*.75 (gamma10);
  		y*1;
  		%between%

  		y on w*.5
              x*1 (gamma01);
  		[y*2];
  		y*.5;

  model constraint:
          new(betac*.25);
          betac = gamma01 - gamma10;

  output:
  		tech9;



INPUT READING TERMINATED NORMALLY



this is an example of a two-level
regression analysis for a continuous
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                                    1
Number of independent variables                                  2
Number of continuous latent variables                            0

Observed dependent variables

  Continuous
   Y

Observed independent variables
   X           W

Variables with special functions

  Between variables
   W


Estimator                                                      MLR
Information matrix                                        OBSERVED
Maximum number of iterations                                   100
Convergence criterion                                    0.100D-05
Maximum number of EM iterations                                500
Convergence criteria for the EM algorithm
  Loglikelihood change                                   0.100D-02
  Relative loglikelihood change                          0.100D-05
  Derivative                                             0.100D-03
Minimum variance                                         0.100D-03
Maximum number of steepest descent iterations                   20
Maximum number of iterations for H1                           2000
Convergence criterion for H1                             0.100D-03
Optimization algorithm                                         EMA


SUMMARY OF DATA FOR THE FIRST REPLICATION

     Cluster information

       Size (s)    Number of clusters of Size s

          5            40
         10            50
         15            20

     Average cluster size        9.091

     Estimated Intraclass Correlations for the Y Variables

                Intraclass
     Variable  Correlation

     Y            0.509


SAMPLE STATISTICS FOR THE FIRST REPLICATION

NOTE:  The sample statistics for within and between refer to the
       maximum-likelihood estimated within and between covariance
       matrices, respectively.


     ESTIMATED SAMPLE STATISTICS FOR WITHIN


           Means
              Y             X             W
              ________      ________      ________
 1              0.000         0.000         0.000


           Covariances
              Y             X             W
              ________      ________      ________
 Y              1.572
 X              0.765         0.981
 W              0.000         0.000         0.000


           Correlations
              Y             X             W
              ________      ________      ________
 Y              1.000
 X              0.616         1.000
 W              0.000         0.000         0.000


     ESTIMATED SAMPLE STATISTICS FOR BETWEEN


           Means
              Y             X             W
              ________      ________      ________
 1              1.980        -0.021        -0.082


           Covariances
              Y             X             W
              ________      ________      ________
 Y              1.633
 X              0.649         0.409
 W              0.888         0.422         1.004


           Correlations
              Y             X             W
              ________      ________      ________
 Y              1.000
 X              0.794         1.000
 W              0.693         0.658         1.000




MODEL FIT INFORMATION

Number of Free Parameters                        6

Loglikelihood

    H0 Value

        Mean                             -2971.585
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        -2971.585      -2971.585
           0.980       0.000        -2971.585      -2971.585
           0.950       0.000        -2971.585      -2971.585
           0.900       0.000        -2971.585      -2971.585
           0.800       0.000        -2971.585      -2971.585
           0.700       0.000        -2971.585      -2971.585
           0.500       0.000        -2971.585      -2971.585
           0.300       0.000        -2971.585      -2971.585
           0.200       0.000        -2971.585      -2971.585
           0.100       0.000        -2971.585      -2971.585
           0.050       0.000        -2971.585      -2971.585
           0.020       0.000        -2971.585      -2971.585
           0.010       0.000        -2971.585      -2971.585

    H1 Value

        Mean                             -2971.585
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        -2971.585      -2971.585
           0.980       0.000        -2971.585      -2971.585
           0.950       0.000        -2971.585      -2971.585
           0.900       0.000        -2971.585      -2971.585
           0.800       0.000        -2971.585      -2971.585
           0.700       0.000        -2971.585      -2971.585
           0.500       0.000        -2971.585      -2971.585
           0.300       0.000        -2971.585      -2971.585
           0.200       0.000        -2971.585      -2971.585
           0.100       0.000        -2971.585      -2971.585
           0.050       0.000        -2971.585      -2971.585
           0.020       0.000        -2971.585      -2971.585
           0.010       0.000        -2971.585      -2971.585

Information Criteria

    Akaike (AIC)

        Mean                              5955.170
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         5955.170       5955.170
           0.980       0.000         5955.170       5955.170
           0.950       0.000         5955.170       5955.170
           0.900       0.000         5955.170       5955.170
           0.800       0.000         5955.170       5955.170
           0.700       0.000         5955.170       5955.170
           0.500       0.000         5955.170       5955.170
           0.300       0.000         5955.170       5955.170
           0.200       0.000         5955.170       5955.170
           0.100       0.000         5955.170       5955.170
           0.050       0.000         5955.170       5955.170
           0.020       0.000         5955.170       5955.170
           0.010       0.000         5955.170       5955.170

    Bayesian (BIC)

        Mean                              5984.616
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         5984.616       5984.616
           0.980       0.000         5984.616       5984.616
           0.950       0.000         5984.616       5984.616
           0.900       0.000         5984.616       5984.616
           0.800       0.000         5984.616       5984.616
           0.700       0.000         5984.616       5984.616
           0.500       0.000         5984.616       5984.616
           0.300       0.000         5984.616       5984.616
           0.200       0.000         5984.616       5984.616
           0.100       0.000         5984.616       5984.616
           0.050       0.000         5984.616       5984.616
           0.020       0.000         5984.616       5984.616
           0.010       0.000         5984.616       5984.616

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

        Mean                              5965.560
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         5965.560       5965.560
           0.980       0.000         5965.560       5965.560
           0.950       0.000         5965.560       5965.560
           0.900       0.000         5965.560       5965.560
           0.800       0.000         5965.560       5965.560
           0.700       0.000         5965.560       5965.560
           0.500       0.000         5965.560       5965.560
           0.300       0.000         5965.560       5965.560
           0.200       0.000         5965.560       5965.560
           0.100       0.000         5965.560       5965.560
           0.050       0.000         5965.560       5965.560
           0.020       0.000         5965.560       5965.560
           0.010       0.000         5965.560       5965.560

Chi-Square Test of Model Fit

        Degrees of freedom                       0

        Mean                                 0.001
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       1.000            0.000          0.001
           0.980       1.000            0.000          0.001
           0.950       1.000            0.000          0.001
           0.900       1.000            0.000          0.001
           0.800       1.000            0.000          0.001
           0.700       1.000            0.000          0.001
           0.500       1.000            0.000          0.001
           0.300       1.000            0.000          0.001
           0.200       1.000            0.000          0.001
           0.100       1.000            0.000          0.001
           0.050       1.000            0.000          0.001
           0.020       1.000            0.000          0.001
           0.010       1.000            0.000          0.001

RMSEA (Root Mean Square Error Of Approximation)

        Mean                                 0.000
        Std Dev                              0.000
        Number of successful computations        1

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

SRMR (Standardized Root Mean Square Residual) for the WITHIN level

        Mean                                 0.000
        Std Dev                              0.000
        Number of successful computations        1

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

SRMR (Standardized Root Mean Square Residual) for the BETWEEN level

        Mean                                 0.000
        Std Dev                              0.000
        Number of successful computations        1

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



MODEL RESULTS

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

 Y          ON
  X                0.750     0.7804     0.0000     0.0323     0.0009 1.000 1.000

 Residual Variances
  Y                1.000     0.9750     0.0000     0.0430     0.0006 1.000 1.000

Between Level

 Y          ON
  W                0.500     0.3844     0.0000     0.1219     0.0134 1.000 1.000
  X                1.000     1.1891     0.0000     0.1766     0.0358 1.000 1.000

 Intercepts
  Y                2.000     2.0362     0.0000     0.0775     0.0013 1.000 1.000

 Residual Variances
  Y                0.500     0.5190     0.0000     0.0849     0.0004 1.000 1.000

 New/Additional Parameters
  BETAC            0.250     0.4087     0.0000     0.1807     0.0252 1.000 1.000


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.110E-02
       (ratio of smallest to largest eigenvalue)


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR WITHIN


           NU
              Y             X             W
              ________      ________      ________
 1                  0             0             0


           LAMBDA
              Y             X             W
              ________      ________      ________
 Y                  0             0             0
 X                  0             0             0
 W                  0             0             0


           THETA
              Y             X             W
              ________      ________      ________
 Y                  0
 X                  0             0
 W                  0             0             0


           ALPHA
              Y             X             W
              ________      ________      ________
 1                  0             0             0


           BETA
              Y             X             W
              ________      ________      ________
 Y                  0             1             0
 X                  0             0             0
 W                  0             0             0


           PSI
              Y             X             W
              ________      ________      ________
 Y                  2
 X                  0             0
 W                  0             0             0


     PARAMETER SPECIFICATION FOR BETWEEN


           NU
              Y             X             W
              ________      ________      ________
 1                  0             0             0


           LAMBDA
              Y             X             W
              ________      ________      ________
 Y                  0             0             0
 X                  0             0             0
 W                  0             0             0


           THETA
              Y             X             W
              ________      ________      ________
 Y                  0
 X                  0             0
 W                  0             0             0


           ALPHA
              Y             X             W
              ________      ________      ________
 1                  3             0             0


           BETA
              Y             X             W
              ________      ________      ________
 Y                  0             4             5
 X                  0             0             0
 W                  0             0             0


           PSI
              Y             X             W
              ________      ________      ________
 Y                  6
 X                  0             0
 W                  0             0             0


     PARAMETER SPECIFICATION FOR THE ADDITIONAL PARAMETERS


           NEW/ADDITIONAL PARAMETERS
              BETAC
              ________
 1                  7


     STARTING VALUES FOR WITHIN


           NU
              Y             X             W
              ________      ________      ________
 1              0.000         0.000         0.000


           LAMBDA
              Y             X             W
              ________      ________      ________
 Y              1.000         0.000         0.000
 X              0.000         1.000         0.000
 W              0.000         0.000         1.000


           THETA
              Y             X             W
              ________      ________      ________
 Y              0.000
 X              0.000         0.000
 W              0.000         0.000         0.000


           ALPHA
              Y             X             W
              ________      ________      ________
 1              0.000         0.000         0.000


           BETA
              Y             X             W
              ________      ________      ________
 Y              0.000         0.750         0.000
 X              0.000         0.000         0.000
 W              0.000         0.000         0.000


           PSI
              Y             X             W
              ________      ________      ________
 Y              1.000
 X              0.000         0.500
 W              0.000         0.000         0.000


     STARTING VALUES FOR BETWEEN


           NU
              Y             X             W
              ________      ________      ________
 1              0.000         0.000         0.000


           LAMBDA
              Y             X             W
              ________      ________      ________
 Y              1.000         0.000         0.000
 X              0.000         1.000         0.000
 W              0.000         0.000         1.000


           THETA
              Y             X             W
              ________      ________      ________
 Y              0.000
 X              0.000         0.000
 W              0.000         0.000         0.000


           ALPHA
              Y             X             W
              ________      ________      ________
 1              2.000         0.000         0.000


           BETA
              Y             X             W
              ________      ________      ________
 Y              0.000         1.000         0.500
 X              0.000         0.000         0.000
 W              0.000         0.000         0.000


           PSI
              Y             X             W
              ________      ________      ________
 Y              0.500
 X              0.000         0.500
 W              0.000         0.000         0.500


     STARTING VALUES FOR THE ADDITIONAL PARAMETERS


           NEW/ADDITIONAL PARAMETERS
              BETAC
              ________
 1              0.250


     POPULATION VALUES FOR WITHIN


           NU
              Y             X             W
              ________      ________      ________
 1              0.000         0.000         0.000


           LAMBDA
              Y             X             W
              ________      ________      ________
 Y              1.000         0.000         0.000
 X              0.000         1.000         0.000
 W              0.000         0.000         1.000


           THETA
              Y             X             W
              ________      ________      ________
 Y              0.000
 X              0.000         0.000
 W              0.000         0.000         0.000


           ALPHA
              Y             X             W
              ________      ________      ________
 1              0.000         0.000         0.000


           BETA
              Y             X             W
              ________      ________      ________
 Y              0.000         0.750         0.000
 X              0.000         0.000         0.000
 W              0.000         0.000         0.000


           PSI
              Y             X             W
              ________      ________      ________
 Y              1.000
 X              0.000         1.000
 W              0.000         0.000         0.000


     POPULATION VALUES FOR BETWEEN


           NU
              Y             X             W
              ________      ________      ________
 1              0.000         0.000         0.000


           LAMBDA
              Y             X             W
              ________      ________      ________
 Y              1.000         0.000         0.000
 X              0.000         1.000         0.000
 W              0.000         0.000         1.000


           THETA
              Y             X             W
              ________      ________      ________
 Y              0.000
 X              0.000         0.000
 W              0.000         0.000         0.000


           ALPHA
              Y             X             W
              ________      ________      ________
 1              2.000         0.000         0.000


           BETA
              Y             X             W
              ________      ________      ________
 Y              0.000         1.000         0.500
 X              0.000         0.000         0.000
 W              0.000         0.000         0.000


           PSI
              Y             X             W
              ________      ________      ________
 Y              0.500
 X              0.000         0.500
 W              0.000         0.500         1.000


TECHNICAL 9 OUTPUT

  Error messages for each replication (if any)



SAVEDATA INFORMATION

  Order of variables

    Y
    X
    W
    CLUSTER

  Save file
    ex9.1b.dat

  Save file format           Free
  Save file record length    10000


     Beginning Time:  22:08:06
        Ending Time:  22:08:07
       Elapsed Time:  00:00:01



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