Mplus VERSION 7.4
MUTHEN & MUTHEN
06/03/2016   3:04 PM

INPUT INSTRUCTIONS

  title:
      Confounding due to omitted c
      resulting in corr(y-residual, m) = 0.1633

  montecarlo:
      names = y m x c;
      nobs = 400;
      nreps = 500;
      repsave = all;
      save = confrep*.dat;
      cutpoints = x(0);

  model population:
      x-c@1; [x-c@0];
      m on x*.5 c*.4;
      y on m*.5 c*.3;
      m*.59;
      y*.54;
      [y*0]; [m*0];


  analysis:

  model:
      m on x*.5 (a)
      c*.4;
      y on m*.5 (b)
      c*.3;
      m*.59;
      y*.54;
      [y*0];
      [m*0];

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

  output:





INPUT READING TERMINATED NORMALLY




Confounding due to omitted c
resulting in corr(y-residual, m) = 0.1633

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                                  2
Number of continuous latent variables                            0

Observed dependent variables

  Continuous
   Y           M

Observed independent variables
   X           C


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             C
              ________      ________      ________      ________
      1         0.163         0.291         0.528         0.073


           Covariances
              Y             M             X             C
              ________      ________      ________      ________
 Y              1.055
 M              0.590         0.863
 X              0.100         0.161         0.249
 C              0.537         0.370         0.033         0.944


           Correlations
              Y             M             X             C
              ________      ________      ________      ________
 Y              1.000
 M              0.618         1.000
 X              0.196         0.347         1.000
 C              0.538         0.410         0.067         1.000


MODEL FIT INFORMATION

Number of Free Parameters                        8

Loglikelihood

    H0 Value

        Mean                              -903.066
        Std Dev                             19.568
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.998         -948.586       -945.076
           0.980       0.986         -943.252       -942.729
           0.950       0.956         -935.253       -933.548
           0.900       0.912         -928.144       -927.152
           0.800       0.786         -919.534       -920.561
           0.700       0.668         -913.327       -914.890
           0.500       0.502         -903.066       -903.049
           0.300       0.294         -892.805       -893.451
           0.200       0.198         -886.598       -887.436
           0.100       0.092         -877.988       -879.040
           0.050       0.058         -870.880       -868.633
           0.020       0.030         -862.880       -860.834
           0.010       0.014         -857.546       -856.275

    H1 Value

        Mean                              -902.604
        Std Dev                             19.584
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.998         -948.163       -944.512
           0.980       0.984         -942.824       -942.560
           0.950       0.956         -934.818       -933.102
           0.900       0.916         -927.703       -926.563
           0.800       0.790         -919.086       -920.248
           0.700       0.674         -912.874       -914.383
           0.500       0.502         -902.604       -902.404
           0.300       0.294         -892.334       -892.770
           0.200       0.198         -886.122       -887.198
           0.100       0.090         -877.505       -878.629
           0.050       0.060         -870.390       -868.484
           0.020       0.028         -862.384       -860.568
           0.010       0.014         -857.046       -856.225

Information Criteria

    Akaike (AIC)

        Mean                              1822.133
        Std Dev                             39.135
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.986         1731.093       1721.578
           0.980       0.970         1741.761       1734.436
           0.950       0.942         1757.759       1753.050
           0.900       0.908         1771.977       1773.896
           0.800       0.802         1789.196       1789.040
           0.700       0.706         1801.610       1802.708
           0.500       0.498         1822.133       1821.826
           0.300       0.332         1842.655       1845.768
           0.200       0.214         1855.069       1856.766
           0.100       0.088         1872.288       1869.807
           0.050       0.044         1886.506       1882.321
           0.020       0.014         1902.504       1901.234
           0.010       0.002         1913.173       1905.033

    Bayesian (BIC)

        Mean                              1854.064
        Std Dev                             39.135
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.986         1763.024       1753.509
           0.980       0.970         1773.692       1766.368
           0.950       0.942         1789.691       1784.982
           0.900       0.908         1803.909       1805.828
           0.800       0.802         1821.128       1820.972
           0.700       0.706         1833.542       1834.640
           0.500       0.498         1854.064       1853.758
           0.300       0.332         1874.587       1877.700
           0.200       0.214         1887.000       1888.698
           0.100       0.088         1904.220       1901.738
           0.050       0.044         1918.438       1914.253
           0.020       0.014         1934.436       1933.165
           0.010       0.002         1945.104       1936.965

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

        Mean                              1828.680
        Std Dev                             39.135
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.986         1737.640       1728.125
           0.980       0.970         1748.308       1740.983
           0.950       0.942         1764.306       1759.597
           0.900       0.908         1778.524       1780.443
           0.800       0.802         1795.744       1795.588
           0.700       0.706         1808.157       1809.255
           0.500       0.498         1828.680       1828.374
           0.300       0.332         1849.202       1852.315
           0.200       0.214         1861.616       1863.313
           0.100       0.088         1878.835       1876.354
           0.050       0.044         1893.053       1888.868
           0.020       0.014         1909.051       1907.781
           0.010       0.002         1919.720       1911.580

Chi-Square Test of Model Fit

        Degrees of freedom                       1

        Mean                                 0.924
        Std Dev                              1.325
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.994            0.000          0.000
           0.980       0.988            0.001          0.001
           0.950       0.948            0.004          0.004
           0.900       0.906            0.016          0.016
           0.800       0.798            0.064          0.058
           0.700       0.690            0.148          0.135
           0.500       0.466            0.455          0.382
           0.300       0.284            1.074          0.989
           0.200       0.184            1.642          1.481
           0.100       0.086            2.706          2.492
           0.050       0.042            3.841          3.414
           0.020       0.018            5.412          4.727
           0.010       0.006            6.635          6.243

RMSEA (Root Mean Square Error Of Approximation)

        Mean                                 0.016
        Std Dev                              0.029
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       1.000           -0.051          0.000
           0.980       1.000           -0.043          0.000
           0.950       1.000           -0.032          0.000
           0.900       1.000           -0.021          0.000
           0.800       1.000           -0.009          0.000
           0.700       0.298            0.001          0.000
           0.500       0.274            0.016          0.000
           0.300       0.214            0.031          0.000
           0.200       0.184            0.040          0.035
           0.100       0.140            0.053          0.061
           0.050       0.092            0.063          0.078
           0.020       0.058            0.075          0.097
           0.010       0.046            0.083          0.114

SRMR (Standardized Root Mean Square Residual)

        Mean                                 0.007
        Std Dev                              0.006
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       1.000           -0.006          0.000
           0.980       1.000           -0.004          0.000
           0.950       1.000           -0.002          0.001
           0.900       0.988            0.000          0.001
           0.800       0.782            0.003          0.002
           0.700       0.620            0.004          0.004
           0.500       0.412            0.007          0.006
           0.300       0.262            0.010          0.010
           0.200       0.194            0.012          0.012
           0.100       0.124            0.014          0.015
           0.050       0.078            0.016          0.018
           0.020       0.038            0.019          0.021
           0.010       0.028            0.020          0.022


MODEL RESULTS

                              ESTIMATES              S. E.     M. S. E.  95%  % Sig
                 Population   Average   Std. Dev.   Average             Cover Coeff
 M        ON
  X                   0.500     0.5009     0.0762     0.0767     0.0058 0.944 1.000
  C                   0.400     0.3996     0.0387     0.0383     0.0015 0.948 1.000

 Y        ON
  M                   0.500     0.4987     0.0463     0.0455     0.0021 0.934 1.000
  C                   0.300     0.3025     0.0417     0.0410     0.0017 0.944 1.000

 Intercepts
  Y                   0.000     0.0009     0.0403     0.0385     0.0016 0.928 0.072
  M                   0.000     0.0010     0.0546     0.0542     0.0030 0.938 0.062

 Residual Variances
  Y                   0.540     0.5376     0.0367     0.0380     0.0014 0.960 1.000
  M                   0.590     0.5856     0.0415     0.0414     0.0017 0.942 1.000

New/Additional Parameters
  IND                 0.250     0.2497     0.0443     0.0447     0.0020 0.948 1.000


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.873E-03
       (ratio of smallest to largest eigenvalue)


TECHNICAL OUTPUT


     PARAMETER SPECIFICATION


           NU
              Y             M             X             C
              ________      ________      ________      ________
      1           0             0             0             0


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


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


           ALPHA
              Y             M             X             C
              ________      ________      ________      ________
      1           1             2             0             0


           BETA
              Y             M             X             C
              ________      ________      ________      ________
 Y                  0             3             0             4
 M                  0             0             5             6
 X                  0             0             0             0
 C                  0             0             0             0


           PSI
              Y             M             X             C
              ________      ________      ________      ________
 Y                  7
 M                  0             8
 X                  0             0             0
 C                  0             0             0             0


     PARAMETER SPECIFICATION FOR THE ADDITIONAL PARAMETERS


           New/Additional Parameters
              IND
              ________
 1                  9


     STARTING VALUES


           NU
              Y             M             X             C
              ________      ________      ________      ________
      1         0.000         0.000         0.000         0.000


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


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


           ALPHA
              Y             M             X             C
              ________      ________      ________      ________
      1         0.000         0.000         0.528         0.073


           BETA
              Y             M             X             C
              ________      ________      ________      ________
 Y              0.000         0.500         0.000         0.300
 M              0.000         0.000         0.500         0.400
 X              0.000         0.000         0.000         0.000
 C              0.000         0.000         0.000         0.000


           PSI
              Y             M             X             C
              ________      ________      ________      ________
 Y              0.540
 M              0.000         0.590
 X              0.000         0.000         0.249
 C              0.000         0.000         0.033         0.944


     STARTING VALUES FOR THE ADDITIONAL PARAMETERS


           New/Additional Parameters
              IND
              ________
 1              0.250


     POPULATION VALUES


           NU
              Y             M             X             C
              ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000


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


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


           ALPHA
              Y             M             X             C
              ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000


           BETA
              Y             M             X             C
              ________      ________      ________      ________
 Y              0.000         0.500         0.000         0.300
 M              0.000         0.000         0.500         0.400
 X              0.000         0.000         0.000         0.000
 C              0.000         0.000         0.000         0.000


           PSI
              Y             M             X             C
              ________      ________      ________      ________
 Y              0.540
 M              0.000         0.590
 X              0.000         0.000         1.000
 C              0.000         0.000         0.000         1.000


SAVEDATA INFORMATION

  Order of variables

    Y
    M
    X
    C

  Save file
    confrep*.dat

  Save file format           Free
  Save file record length    10000


DIAGRAM INFORMATION

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


     Beginning Time:  15:04:20
        Ending Time:  15:04:22
       Elapsed Time:  00:00:02



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