Mplus VERSION 6
MUTHEN & MUTHEN
04/25/2010  11:31 PM

INPUT INSTRUCTIONS

  title:
      web6ex1.inp

  montecarlo:
      names are y1 y2 y3 y4 x;
      nobs=400;
      nrep=500;

  analysis:
      type=random;

  model montecarlo:
      x@1; [x@0];
      eta2 by y3@1 y4*1;
      eta2*1;
      y3-y4*0.25; !Reliability = 0.80
      eta1 on eta2*0.4;
      eta1 on x*0.0; !No main effect
      eta1*0.5;
      eta1 by y1@1 y2*1;
      y1-y2*0.25; !Reliability approx 0.80
      s | eta1 on x;
      s on eta2*0.15; s@0; [s@0]; !This defines s = beta_3 * eta_2
      !uncorrelated eta_2 and x

  model:
      eta2 by y3@1 y4*1;
      eta2*1;
      y3-y4*0.25; !Reliability = 0.80
      eta1 on eta2*0.4;
      eta1 on x*0.0; !No main effect
      eta1*0.5;
      eta1 by y1@1 y2*1;
      y1-y2*0.25; !Reliability approx 0.80
      s | eta1 on x;
      s on eta2*0.15; s@0; [s@0]; !This defines s = beta_3 * eta_2
      !uncorrelated eta_2 and x

  output:
      tech9;



INPUT READING TERMINATED NORMALLY




web6ex1.inp

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         400

Number of replications
    Requested                                                  500
    Completed                                                  500
Value of seed                                                    0

Number of dependent variables                                    4
Number of independent variables                                  1
Number of continuous latent variables                            3

Observed dependent variables

  Continuous
   Y1          Y2          Y3          Y4

Observed independent variables
   X

Continuous latent variables
   ETA2        ETA1        S


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
Optimization algorithm                                         EMA


SAMPLE STATISTICS FOR THE FIRST REPLICATION


     ESTIMATED SAMPLE STATISTICS


           Means
              Y1            Y2            Y3            Y4            X
              ________      ________      ________      ________      ________
 1             -0.022        -0.037        -0.045        -0.007         0.032


           Covariances
              Y1            Y2            Y3            Y4            X
              ________      ________      ________      ________      ________
 Y1             0.918
 Y2             0.714         0.993
 Y3             0.390         0.511         1.282
 Y4             0.350         0.411         0.955         1.174
 X             -0.107        -0.127        -0.049        -0.029         0.957


           Correlations
              Y1            Y2            Y3            Y4            X
              ________      ________      ________      ________      ________
 Y1             1.000
 Y2             0.748         1.000
 Y3             0.359         0.453         1.000
 Y4             0.337         0.381         0.779         1.000
 X             -0.114        -0.130        -0.044        -0.028         1.000




TESTS OF MODEL FIT

Number of Free Parameters                       15

Loglikelihood

    H0 Value

        Mean                             -1921.331
        Std Dev                             27.689
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.994        -1985.743      -1982.798
           0.980       0.984        -1978.195      -1977.453
           0.950       0.962        -1966.876      -1963.161
           0.900       0.910        -1956.817      -1956.343
           0.800       0.802        -1944.634      -1944.895
           0.700       0.678        -1935.851      -1937.943
           0.500       0.476        -1921.331      -1923.418
           0.300       0.292        -1906.811      -1907.663
           0.200       0.192        -1898.028      -1899.023
           0.100       0.112        -1885.845      -1884.244
           0.050       0.050        -1875.785      -1875.865
           0.020       0.024        -1864.466      -1858.350
           0.010       0.016        -1856.918      -1853.754

Information Criteria

    Akaike (AIC)

        Mean                              3872.662
        Std Dev                             55.378
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.984         3743.837       3735.603
           0.980       0.976         3758.933       3746.388
           0.950       0.950         3781.571       3781.198
           0.900       0.888         3801.690       3796.894
           0.800       0.808         3826.056       3826.896
           0.700       0.708         3843.622       3844.320
           0.500       0.524         3872.662       3876.068
           0.300       0.322         3901.702       3905.642
           0.200       0.198         3919.267       3919.109
           0.100       0.090         3943.633       3940.873
           0.050       0.038         3963.752       3956.203
           0.020       0.016         3986.390       3978.127
           0.010       0.006         4001.486       3993.902

    Bayesian (BIC)

        Mean                              3932.534
        Std Dev                             55.378
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.984         3803.709       3795.475
           0.980       0.976         3818.805       3806.260
           0.950       0.950         3841.443       3841.070
           0.900       0.888         3861.562       3856.766
           0.800       0.808         3885.928       3886.768
           0.700       0.708         3903.494       3904.192
           0.500       0.524         3932.534       3935.940
           0.300       0.322         3961.574       3965.513
           0.200       0.198         3979.139       3978.981
           0.100       0.090         4003.505       4000.745
           0.050       0.038         4023.624       4016.075
           0.020       0.016         4046.262       4037.999
           0.010       0.006         4061.358       4053.774

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

        Mean                              3884.938
        Std Dev                             55.378
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.984         3756.113       3747.879
           0.980       0.976         3771.209       3758.664
           0.950       0.950         3793.847       3793.474
           0.900       0.888         3813.966       3809.170
           0.800       0.808         3838.332       3839.172
           0.700       0.708         3855.898       3856.596
           0.500       0.524         3884.938       3888.344
           0.300       0.322         3913.978       3917.917
           0.200       0.198         3931.543       3931.385
           0.100       0.090         3955.909       3953.149
           0.050       0.038         3976.028       3968.479
           0.020       0.016         3998.666       3990.403
           0.010       0.006         4013.762       4006.178



MODEL RESULTS

                           ESTIMATES              S. E.     M. S. E.  95%  % Sig
              Population   Average   Std. Dev.   Average             Cover Coeff
 ETA2     BY
  Y3               1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y4               1.000     1.0054     0.0769     0.0784     0.0059 0.962 1.000

 ETA1     BY
  Y1               1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y2               1.000     1.0041     0.0907     0.0919     0.0082 0.952 1.000

 ETA1       ON
  ETA2             0.400     0.4020     0.0506     0.0491     0.0026 0.930 1.000

 S          ON
  ETA2             0.150     0.1469     0.0437     0.0443     0.0019 0.942 0.912

 ETA1       ON
  X                0.000     0.0006     0.0401     0.0413     0.0016 0.950 0.050

 Intercepts
  Y1               0.000     0.0019     0.0480     0.0477     0.0023 0.948 0.052
  Y2               0.000     0.0023     0.0457     0.0476     0.0021 0.958 0.042
  Y3               0.000     0.0011     0.0564     0.0557     0.0032 0.948 0.052
  Y4               0.000     0.0019     0.0556     0.0558     0.0031 0.948 0.052
  S                0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

 Variances
  ETA2             1.000     0.9942     0.1109     0.1108     0.0123 0.956 1.000

 Residual Variances
  Y1               0.250     0.2475     0.0579     0.0585     0.0034 0.958 0.976
  Y2               0.250     0.2459     0.0591     0.0584     0.0035 0.958 0.958
  Y3               0.250     0.2485     0.0722     0.0718     0.0052 0.956 0.894
  Y4               0.250     0.2464     0.0730     0.0718     0.0053 0.958 0.902
  ETA1             0.500     0.4948     0.0626     0.0649     0.0039 0.938 1.000
  S                0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.931E-02
       (ratio of smallest to largest eigenvalue)


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION


           NU
              Y1            Y2            Y3            Y4            X
              ________      ________      ________      ________      ________
 1                  1             2             3             4             0


           LAMBDA
              ETA2          ETA1          S             X
              ________      ________      ________      ________
 Y1                 0             0             0             0
 Y2                 0             5             0             0
 Y3                 0             0             0             0
 Y4                 6             0             0             0
 X                  0             0             0             0


           THETA
              Y1            Y2            Y3            Y4            X
              ________      ________      ________      ________      ________
 Y1                 7
 Y2                 0             8
 Y3                 0             0             9
 Y4                 0             0             0            10
 X                  0             0             0             0             0


           ALPHA
              ETA2          ETA1          S             X
              ________      ________      ________      ________
 1                  0             0             0             0


           BETA
              ETA2          ETA1          S             X
              ________      ________      ________      ________
 ETA2               0             0             0             0
 ETA1              11             0             0            12
 S                 13             0             0             0
 X                  0             0             0             0


           PSI
              ETA2          ETA1          S             X
              ________      ________      ________      ________
 ETA2              14
 ETA1               0            15
 S                  0             0             0
 X                  0             0             0             0


     STARTING VALUES


           NU
              Y1            Y2            Y3            Y4            X
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           LAMBDA
              ETA2          ETA1          S             X
              ________      ________      ________      ________
 Y1             0.000         1.000         0.000         0.000
 Y2             0.000         1.000         0.000         0.000
 Y3             1.000         0.000         0.000         0.000
 Y4             1.000         0.000         0.000         0.000
 X              0.000         0.000         0.000         1.000


           THETA
              Y1            Y2            Y3            Y4            X
              ________      ________      ________      ________      ________
 Y1             0.250
 Y2             0.000         0.250
 Y3             0.000         0.000         0.250
 Y4             0.000         0.000         0.000         0.250
 X              0.000         0.000         0.000         0.000         0.000


           ALPHA
              ETA2          ETA1          S             X
              ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000


           BETA
              ETA2          ETA1          S             X
              ________      ________      ________      ________
 ETA2           0.000         0.000         0.000         0.000
 ETA1           0.400         0.000         0.000         0.000
 S              0.150         0.000         0.000         0.000
 X              0.000         0.000         0.000         0.000


           PSI
              ETA2          ETA1          S             X
              ________      ________      ________      ________
 ETA2           1.000
 ETA1           0.000         0.500
 S              0.000         0.000         0.000
 X              0.000         0.000         0.000         0.500


     POPULATION VALUES


           NU
              Y1            Y2            Y3            Y4            X
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           LAMBDA
              ETA2          ETA1          S             X
              ________      ________      ________      ________
 Y1             0.000         1.000         0.000         0.000
 Y2             0.000         1.000         0.000         0.000
 Y3             1.000         0.000         0.000         0.000
 Y4             1.000         0.000         0.000         0.000
 X              0.000         0.000         0.000         1.000


           THETA
              Y1            Y2            Y3            Y4            X
              ________      ________      ________      ________      ________
 Y1             0.250
 Y2             0.000         0.250
 Y3             0.000         0.000         0.250
 Y4             0.000         0.000         0.000         0.250
 X              0.000         0.000         0.000         0.000         0.000


           ALPHA
              ETA2          ETA1          S             X
              ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000


           BETA
              ETA2          ETA1          S             X
              ________      ________      ________      ________
 ETA2           0.000         0.000         0.000         0.000
 ETA1           0.400         0.000         0.000         0.000
 S              0.150         0.000         0.000         0.000
 X              0.000         0.000         0.000         0.000


           PSI
              ETA2          ETA1          S             X
              ________      ________      ________      ________
 ETA2           1.000
 ETA1           0.000         0.500
 S              0.000         0.000         0.000
 X              0.000         0.000         0.000         1.000


TECHNICAL 9 OUTPUT

  Error messages for each replication (if any)



     Beginning Time:  23:31:31
        Ending Time:  23:34:29
       Elapsed Time:  00:02:58



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