Mplus VERSION 7.4
MUTHEN & MUTHEN
06/03/2016   3:37 PM

INPUT INSTRUCTIONS

  title:
      Measurement error in M
      with reliability 0.7

  montecarlo:
      names = y m x;
      nobs = 400;
      nreps = 500;
      cutpoints = x(0);

  model population:
      x@1; ! V(dich'd x) = 0.5*0.5 = 0.25
      eta by m@1;
      eta on x*.5;
      eta*.1458; ! V(eta) = 0.0625+0.1458=0.2083, R2(eta) = 0.3
      m*.0893; ! Reliability of m = 0.7

      y on eta*.5 x*.3;
      y*.8879; ! V(y) = 0.112075+0.8879 = 1, R2(y) = 0.11

  analysis:

  model:
      m on x*.5 (b);
      y on m*.5 (a)
      x*.3;
      m*.0893;
      y*.8879;
      [y*0];
      [m*0];

  model constraint:
      new(ind*.25);
      ind = a*b;

  output:





INPUT READING TERMINATED NORMALLY




Measurement error in M
with reliability 0.7

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                                    2
Number of independent variables                                  1
Number of continuous latent variables                            0

Observed dependent variables

  Continuous
   Y           M

Observed independent variables
   X


Estimator                                                       ML
Information matrix                                        OBSERVED
Maximum number of iterations                                  1000
Convergence criterion                                    0.500D-04
Maximum number of steepest descent iterations                   20



SAMPLE STATISTICS FOR THE FIRST REPLICATION


     SAMPLE STATISTICS


           Means
              Y             M             X
              ________      ________      ________
      1         0.305         0.254         0.487


           Covariances
              Y             M             X
              ________      ________      ________
 Y              0.992
 M              0.172         0.298
 X              0.156         0.117         0.250


           Correlations
              Y             M             X
              ________      ________      ________
 Y              1.000
 M              0.317         1.000
 X              0.312         0.428         1.000


MODEL FIT INFORMATION

Number of Free Parameters                        7

Loglikelihood

    H0 Value

        Mean                              -822.412
        Std Dev                             18.926
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.992         -866.440       -866.138
           0.980       0.982         -861.281       -860.486
           0.950       0.958         -853.544       -852.108
           0.900       0.904         -846.668       -846.588
           0.800       0.796         -838.340       -838.885
           0.700       0.706         -832.337       -832.090
           0.500       0.496         -822.412       -822.796
           0.300       0.290         -812.487       -813.288
           0.200       0.202         -806.484       -806.423
           0.100       0.096         -798.156       -798.303
           0.050       0.060         -791.280       -790.008
           0.020       0.024         -783.543       -781.651
           0.010       0.010         -778.384       -778.525

    H1 Value

        Mean                              -822.412
        Std Dev                             18.926
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.992         -866.440       -866.138
           0.980       0.982         -861.281       -860.486
           0.950       0.958         -853.544       -852.108
           0.900       0.904         -846.668       -846.588
           0.800       0.796         -838.340       -838.885
           0.700       0.706         -832.337       -832.090
           0.500       0.496         -822.412       -822.796
           0.300       0.290         -812.487       -813.288
           0.200       0.202         -806.484       -806.423
           0.100       0.096         -798.156       -798.303
           0.050       0.060         -791.280       -790.008
           0.020       0.024         -783.543       -781.651
           0.010       0.010         -778.384       -778.525

Information Criteria

    Akaike (AIC)

        Mean                              1658.824
        Std Dev                             37.852
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.990         1570.768       1568.611
           0.980       0.976         1581.086       1577.254
           0.950       0.940         1596.560       1591.683
           0.900       0.904         1610.312       1610.328
           0.800       0.798         1626.967       1625.885
           0.700       0.710         1638.974       1640.360
           0.500       0.504         1658.824       1659.490
           0.300       0.294         1678.674       1677.868
           0.200       0.204         1690.680       1691.665
           0.100       0.096         1707.335       1706.751
           0.050       0.042         1721.087       1717.737
           0.020       0.018         1736.561       1734.639
           0.010       0.008         1746.880       1740.174

    Bayesian (BIC)

        Mean                              1686.764
        Std Dev                             37.852
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.990         1598.708       1596.552
           0.980       0.976         1609.027       1605.194
           0.950       0.940         1624.501       1619.624
           0.900       0.904         1638.252       1638.269
           0.800       0.798         1654.907       1653.825
           0.700       0.710         1666.914       1668.300
           0.500       0.504         1686.764       1687.430
           0.300       0.294         1706.614       1705.808
           0.200       0.204         1718.621       1719.605
           0.100       0.096         1735.276       1734.691
           0.050       0.042         1749.027       1745.678
           0.020       0.018         1764.501       1762.579
           0.010       0.008         1774.820       1768.114

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

        Mean                              1664.553
        Std Dev                             37.852
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.990         1576.497       1574.340
           0.980       0.976         1586.815       1582.983
           0.950       0.940         1602.289       1597.412
           0.900       0.904         1616.041       1616.057
           0.800       0.798         1632.696       1631.613
           0.700       0.710         1644.703       1646.089
           0.500       0.504         1664.553       1665.219
           0.300       0.294         1684.402       1683.596
           0.200       0.204         1696.409       1697.393
           0.100       0.096         1713.064       1712.480
           0.050       0.042         1726.816       1723.466
           0.020       0.018         1742.290       1740.367
           0.010       0.008         1752.608       1745.903

Chi-Square Test of Model Fit

        Degrees of freedom                       0

        Mean                                 0.000
        Std Dev                              0.000
        Number of successful computations      500

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

RMSEA (Root Mean Square Error Of Approximation)

        Mean                                 0.000
        Std Dev                              0.000
        Number of successful computations      500

             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)

        Mean                                 0.000
        Std Dev                              0.000
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.954            0.000          0.000
           0.980       0.954            0.000          0.000
           0.950       0.954            0.000          0.000
           0.900       0.952            0.000          0.000
           0.800       0.942            0.000          0.000
           0.700       0.880            0.000          0.000
           0.500       0.620            0.000          0.000
           0.300       0.270            0.000          0.000
           0.200       0.068            0.000          0.000
           0.100       0.002            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
 M        ON
  X                   0.500     0.4983     0.0496     0.0484     0.0025 0.942 1.000

 Y        ON
  M                   0.500     0.3071     0.1024     0.0980     0.0477 0.488 0.876
  X                   0.300     0.4020     0.1068     0.1068     0.0218 0.832 0.962

 Intercepts
  Y                   0.000     0.0016     0.0694     0.0670     0.0048 0.944 0.056
  M                   0.000    -0.0004     0.0359     0.0342     0.0013 0.940 0.060

 Residual Variances
  Y                   0.888     0.8981     0.0608     0.0635     0.0038 0.958 1.000
  M                   0.089     0.2342     0.0167     0.0166     0.0213 0.000 1.000

New/Additional Parameters
  IND                 0.250     0.1526     0.0524     0.0513     0.0122 0.502 0.868


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.268E-03
       (ratio of smallest to largest eigenvalue)


TECHNICAL OUTPUT


     PARAMETER SPECIFICATION


           NU
              Y             M             X
              ________      ________      ________
      1           0             0             0


           LAMBDA
              Y             M             X
              ________      ________      ________
 Y                  0             0             0
 M                  0             0             0
 X                  0             0             0


           THETA
              Y             M             X
              ________      ________      ________
 Y                  0
 M                  0             0
 X                  0             0             0


           ALPHA
              Y             M             X
              ________      ________      ________
      1           1             2             0


           BETA
              Y             M             X
              ________      ________      ________
 Y                  0             3             4
 M                  0             0             5
 X                  0             0             0


           PSI
              Y             M             X
              ________      ________      ________
 Y                  6
 M                  0             7
 X                  0             0             0


     PARAMETER SPECIFICATION FOR THE ADDITIONAL PARAMETERS


           New/Additional Parameters
              IND
              ________
 1                  8


     STARTING VALUES


           NU
              Y             M             X
              ________      ________      ________
      1         0.000         0.000         0.000


           LAMBDA
              Y             M             X
              ________      ________      ________
 Y              1.000         0.000         0.000
 M              0.000         1.000         0.000
 X              0.000         0.000         1.000


           THETA
              Y             M             X
              ________      ________      ________
 Y              0.000
 M              0.000         0.000
 X              0.000         0.000         0.000


           ALPHA
              Y             M             X
              ________      ________      ________
      1         0.000         0.000         0.487


           BETA
              Y             M             X
              ________      ________      ________
 Y              0.000         0.500         0.300
 M              0.000         0.000         0.500
 X              0.000         0.000         0.000


           PSI
              Y             M             X
              ________      ________      ________
 Y              0.888
 M              0.000         0.089
 X              0.000         0.000         0.250


     STARTING VALUES FOR THE ADDITIONAL PARAMETERS


           New/Additional Parameters
              IND
              ________
 1              0.250


     POPULATION VALUES


           NU
              Y             M             X
              ________      ________      ________
 1              0.000         0.000         0.000


           LAMBDA
              ETA           Y             X
              ________      ________      ________
 Y              0.000         1.000         0.000
 M              1.000         0.000         0.000
 X              0.000         0.000         1.000


           THETA
              Y             M             X
              ________      ________      ________
 Y              0.000
 M              0.000         0.089
 X              0.000         0.000         0.000


           ALPHA
              ETA           Y             X
              ________      ________      ________
 1              0.000         0.000         0.000


           BETA
              ETA           Y             X
              ________      ________      ________
 ETA            0.000         0.000         0.500
 Y              0.500         0.000         0.300
 X              0.000         0.000         0.000


           PSI
              ETA           Y             X
              ________      ________      ________
 ETA            0.146
 Y              0.000         0.888
 X              0.000         0.000         1.000


DIAGRAM INFORMATION

  Mplus diagrams are currently not available for Monte Carlo analysis.
  No diagram output was produced.


     Beginning Time:  15:37:05
        Ending Time:  15:37:06
       Elapsed Time:  00:00:01



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