Mplus VERSION 7.3
MUTHEN & MUTHEN
09/22/2014   5:44 PM

INPUT INSTRUCTIONS

  TITLE:	this is an example of a Monte Carlo
  	simulation study for a linear growth model
  	for a continuous outcome with missing data
  	where attrition is	predicted by time-
  	invariant covariates (MAR)
  MONTECARLO:
  	NAMES ARE y1-y4 x1 x2;
  	NOBSERVATIONS = 500;
  	NREPS = 500;
  	SEED = 4533;
  	CUTPOINTS = x2(1);
  	MISSING = y1-y4;
  MODEL POPULATION:
  	x1-x2@1;
  	[x1-x2@0];	
  	i s | y1@0 y2@1 y3@2 y4@3;
  	[i*1 s*2];
  	i*1; s*.2; i WITH s*.1;
  	y1-y4*.5;
  	i ON x1*1 x2*.5;
  	s ON x1*.4 x2*.25;
  MODEL MISSING:
  	[y1-y4@-1];
  	y1 ON x1*.4 x2*.2;
  	y2 ON x1*.8 x2*.4;
  	y3 ON x1*1.6 x2*.8;
  	y4 ON x1*3.2 x2*1.6;
  MODEL:	i s | y1@0 y2@1 y3@2 y4@3;
  	[i*1 s*2];
  	i*1; s*.2; i WITH s*.1;
  	y1-y4*.5;
  	i ON x1*1 x2*.5;
  	s ON x1*.4 x2*.25;
  OUTPUT:	TECH9;



INPUT READING TERMINATED NORMALLY



this is an example of a Monte Carlo
simulation study for a linear growth model
for a continuous outcome with missing data
where attrition is predicted by time-
invariant covariates (MAR)

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         500

Number of replications
    Requested                                                  500
    Completed                                                  500
Value of seed                                                 4533

Number of dependent variables                                    4
Number of independent variables                                  2
Number of continuous latent variables                            2

Observed dependent variables

  Continuous
   Y1          Y2          Y3          Y4

Observed independent variables
   X1          X2

Continuous latent variables
   I           S


Estimator                                                       ML
Information matrix                                        OBSERVED
Maximum number of iterations                                  1000
Convergence criterion                                    0.500D-04
Maximum number of steepest descent iterations                   20
Maximum number of iterations for H1                           2000
Convergence criterion for H1                             0.100D-03


SUMMARY OF DATA FOR THE FIRST REPLICATION

     Number of missing data patterns            15


SUMMARY OF MISSING DATA PATTERNS FOR THE FIRST REPLICATION


     MISSING DATA PATTERNS (x = not missing)

           1  2  3  4  5  6  7  8  9 10 11 12 13 14 15
 Y1        x  x  x  x  x  x  x  x
 Y2        x  x  x  x              x  x  x  x
 Y3        x  x        x  x        x  x        x  x
 Y4        x     x     x     x     x     x     x     x
 X1        x  x  x  x  x  x  x  x  x  x  x  x  x  x  x
 X2        x  x  x  x  x  x  x  x  x  x  x  x  x  x  x


     MISSING DATA PATTERN FREQUENCIES

    Pattern   Frequency     Pattern   Frequency     Pattern   Frequency
          1         139           6          30          11          13
          2          40           7          11          12          20
          3          27           8          32          13          10
          4          42           9          45          14          15
          5          45          10          25          15           6


COVARIANCE COVERAGE OF DATA FOR THE FIRST REPLICATION

Minimum covariance coverage value   0.100


     PROPORTION OF DATA PRESENT


           Covariance Coverage
              Y1            Y2            Y3            Y4            X1
              ________      ________      ________      ________      ________
 Y1             0.732
 Y2             0.496         0.702
 Y3             0.508         0.498         0.698
 Y4             0.444         0.448         0.478         0.592
 X1             0.732         0.702         0.698         0.592         1.000
 X2             0.732         0.702         0.698         0.592         1.000


           Covariance Coverage
              X2
              ________
 X2             1.000



SAMPLE STATISTICS FOR THE FIRST REPLICATION


     ESTIMATED SAMPLE STATISTICS


           Means
              Y1            Y2            Y3            Y4            X1
              ________      ________      ________      ________      ________
      1         1.110         3.078         5.038         7.107        -0.018


           Means
              X2
              ________
      1         0.126


           Covariances
              Y1            Y2            Y3            Y4            X1
              ________      ________      ________      ________      ________
 Y1             2.681
 Y2             2.575         3.781
 Y3             3.060         4.011         5.425
 Y4             3.631         4.938         6.321         8.586
 X1             0.920         1.248         1.561         2.022         0.880
 X2             0.012         0.005         0.024         0.040        -0.027


           Covariances
              X2
              ________
 X2             0.110


           Correlations
              Y1            Y2            Y3            Y4            X1
              ________      ________      ________      ________      ________
 Y1             1.000
 Y2             0.809         1.000
 Y3             0.802         0.886         1.000
 Y4             0.757         0.867         0.926         1.000
 X1             0.599         0.684         0.714         0.736         1.000
 X2             0.022         0.008         0.031         0.042        -0.087


           Correlations
              X2
              ________
 X2             1.000


     MAXIMUM LOG-LIKELIHOOD VALUE FOR THE UNRESTRICTED (H1) MODEL IS -2958.775


MODEL FIT INFORMATION

Number of Free Parameters                       13

Loglikelihood

    H0 Value

        Mean                             -2156.302
        Std Dev                             41.768
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.990        -2253.466      -2262.670
           0.980       0.980        -2242.080      -2247.081
           0.950       0.950        -2225.005      -2225.327
           0.900       0.886        -2209.831      -2211.278
           0.800       0.790        -2191.453      -2194.399
           0.700       0.692        -2178.205      -2179.344
           0.500       0.540        -2156.302      -2152.975
           0.300       0.308        -2134.399      -2132.892
           0.200       0.202        -2121.150      -2120.652
           0.100       0.106        -2102.773      -2101.748
           0.050       0.038        -2087.598      -2092.016
           0.020       0.016        -2070.524      -2079.359
           0.010       0.008        -2059.138      -2066.564

    H1 Value

        Mean                             -2151.696
        Std Dev                             41.802
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.988        -2248.938      -2257.355
           0.980       0.980        -2237.543      -2241.302
           0.950       0.948        -2220.455      -2221.494
           0.900       0.894        -2205.268      -2206.349
           0.800       0.792        -2186.876      -2190.004
           0.700       0.688        -2173.616      -2174.889
           0.500       0.540        -2151.696      -2148.003
           0.300       0.308        -2129.775      -2129.445
           0.200       0.210        -2116.515      -2114.266
           0.100       0.104        -2098.123      -2097.787
           0.050       0.036        -2082.936      -2087.567
           0.020       0.016        -2065.848      -2074.406
           0.010       0.006        -2054.453      -2062.106

Information Criteria

    Akaike (AIC)

        Mean                              4338.604
        Std Dev                             83.535
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.992         4144.276       4156.429
           0.980       0.984         4167.048       4179.672
           0.950       0.962         4201.197       4208.183
           0.900       0.894         4231.545       4228.779
           0.800       0.798         4268.300       4265.444
           0.700       0.692         4294.798       4291.709
           0.500       0.460         4338.604       4331.444
           0.300       0.308         4382.409       4384.098
           0.200       0.210         4408.907       4414.276
           0.100       0.114         4445.662       4447.893
           0.050       0.050         4476.010       4475.704
           0.020       0.020         4510.160       4500.917
           0.010       0.010         4532.931       4530.484

    Bayesian (BIC)

        Mean                              4393.393
        Std Dev                             83.535
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.992         4199.066       4211.219
           0.980       0.984         4221.838       4234.462
           0.950       0.962         4255.987       4262.973
           0.900       0.894         4286.335       4283.569
           0.800       0.798         4323.090       4320.233
           0.700       0.692         4349.588       4346.498
           0.500       0.460         4393.393       4386.234
           0.300       0.308         4437.199       4438.888
           0.200       0.210         4463.697       4469.066
           0.100       0.114         4500.452       4502.683
           0.050       0.050         4530.800       4530.494
           0.020       0.020         4564.949       4555.707
           0.010       0.010         4587.721       4585.273

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

        Mean                              4352.131
        Std Dev                             83.535
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.992         4157.803       4169.957
           0.980       0.984         4180.575       4193.199
           0.950       0.962         4214.724       4221.710
           0.900       0.894         4245.072       4242.307
           0.800       0.798         4281.828       4278.971
           0.700       0.692         4308.325       4305.236
           0.500       0.460         4352.131       4344.972
           0.300       0.308         4395.936       4397.625
           0.200       0.210         4422.434       4427.803
           0.100       0.114         4459.189       4461.420
           0.050       0.050         4489.537       4489.231
           0.020       0.020         4523.687       4514.444
           0.010       0.010         4546.458       4544.011

Chi-Square Test of Model Fit

        Degrees of freedom                       9

        Mean                                 9.213
        Std Dev                              4.538
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.992            2.088          2.304
           0.980       0.986            2.532          2.723
           0.950       0.956            3.325          3.361
           0.900       0.896            4.168          4.087
           0.800       0.812            5.380          5.474
           0.700       0.726            6.393          6.506
           0.500       0.510            8.343          8.460
           0.300       0.328           10.656         11.034
           0.200       0.208           12.242         12.431
           0.100       0.100           14.684         14.626
           0.050       0.068           16.919         18.364
           0.020       0.034           19.679         21.149
           0.010       0.012           21.666         21.826

RMSEA (Root Mean Square Error Of Approximation)

        Mean                                 0.012
        Std Dev                              0.016
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       1.000           -0.025          0.000
           0.980       1.000           -0.021          0.000
           0.950       1.000           -0.014          0.000
           0.900       1.000           -0.008          0.000
           0.800       1.000           -0.001          0.000
           0.700       0.438            0.004          0.000
           0.500       0.400            0.012          0.000
           0.300       0.308            0.021          0.021
           0.200       0.222            0.026          0.028
           0.100       0.120            0.033          0.035
           0.050       0.076            0.039          0.046
           0.020       0.052            0.045          0.052
           0.010       0.034            0.050          0.053

SRMR (Standardized Root Mean Square Residual)

        Mean                                 0.015
        Std Dev                              0.005
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       1.000            0.003          0.006
           0.980       0.996            0.004          0.006
           0.950       0.978            0.006          0.007
           0.900       0.922            0.008          0.009
           0.800       0.806            0.010          0.011
           0.700       0.686            0.012          0.012
           0.500       0.442            0.015          0.014
           0.300       0.256            0.018          0.017
           0.200       0.180            0.019          0.019
           0.100       0.114            0.022          0.022
           0.050       0.072            0.023          0.024
           0.020       0.040            0.026          0.028
           0.010       0.024            0.027          0.029


MODEL RESULTS

                              ESTIMATES              S. E.     M. S. E.  95%  % Sig
                 Population   Average   Std. Dev.   Average             Cover Coeff
 I        |
  Y1                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y2                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y3                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y4                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000

 S        |
  Y1                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y2                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y3                  2.000     2.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y4                  3.000     3.0000     0.0000     0.0000     0.0000 1.000 0.000

 I        ON
  X1                  1.000     1.0013     0.0571     0.0578     0.0033 0.956 1.000
  X2                  0.500     0.5003     0.1578     0.1566     0.0249 0.950 0.886

 S        ON
  X1                  0.400     0.3996     0.0346     0.0348     0.0012 0.954 1.000
  X2                  0.250     0.2475     0.0844     0.0873     0.0071 0.952 0.844

 I        WITH
  S                   0.100     0.1030     0.0417     0.0434     0.0017 0.956 0.682

 Intercepts
  Y1                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y2                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y3                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y4                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  I                   1.000     0.9980     0.0648     0.0612     0.0042 0.924 1.000
  S                   2.000     2.0009     0.0339     0.0341     0.0011 0.948 1.000

 Residual Variances
  Y1                  0.500     0.5038     0.0805     0.0843     0.0065 0.952 1.000
  Y2                  0.500     0.5023     0.0583     0.0559     0.0034 0.938 1.000
  Y3                  0.500     0.4974     0.0673     0.0664     0.0045 0.940 1.000
  Y4                  0.500     0.4976     0.1199     0.1161     0.0143 0.932 0.992
  I                   1.000     0.9929     0.1112     0.1092     0.0124 0.938 1.000
  S                   0.200     0.1974     0.0282     0.0288     0.0008 0.958 1.000


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.154E-01
       (ratio of smallest to largest eigenvalue)


TECHNICAL OUTPUT


     PARAMETER SPECIFICATION


           NU
              Y1            Y2            Y3            Y4            X1
              ________      ________      ________      ________      ________
      1           0             0             0             0             0


           NU
              X2
              ________
      1           0


           LAMBDA
              I             S             X1            X2
              ________      ________      ________      ________
 Y1                 0             0             0             0
 Y2                 0             0             0             0
 Y3                 0             0             0             0
 Y4                 0             0             0             0
 X1                 0             0             0             0
 X2                 0             0             0             0


           THETA
              Y1            Y2            Y3            Y4            X1
              ________      ________      ________      ________      ________
 Y1                 1
 Y2                 0             2
 Y3                 0             0             3
 Y4                 0             0             0             4
 X1                 0             0             0             0             0
 X2                 0             0             0             0             0


           THETA
              X2
              ________
 X2                 0


           ALPHA
              I             S             X1            X2
              ________      ________      ________      ________
      1           5             6             0             0


           BETA
              I             S             X1            X2
              ________      ________      ________      ________
 I                  0             0             7             8
 S                  0             0             9            10
 X1                 0             0             0             0
 X2                 0             0             0             0


           PSI
              I             S             X1            X2
              ________      ________      ________      ________
 I                 11
 S                 12            13
 X1                 0             0             0
 X2                 0             0             0             0


     STARTING VALUES


           NU
              Y1            Y2            Y3            Y4            X1
              ________      ________      ________      ________      ________
      1         0.000         0.000         0.000         0.000         0.000


           NU
              X2
              ________
      1         0.000


           LAMBDA
              I             S             X1            X2
              ________      ________      ________      ________
 Y1             1.000         0.000         0.000         0.000
 Y2             1.000         1.000         0.000         0.000
 Y3             1.000         2.000         0.000         0.000
 Y4             1.000         3.000         0.000         0.000
 X1             0.000         0.000         1.000         0.000
 X2             0.000         0.000         0.000         1.000


           THETA
              Y1            Y2            Y3            Y4            X1
              ________      ________      ________      ________      ________
 Y1             0.500
 Y2             0.000         0.500
 Y3             0.000         0.000         0.500
 Y4             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


           THETA
              X2
              ________
 X2             0.000


           ALPHA
              I             S             X1            X2
              ________      ________      ________      ________
      1         1.000         2.000        -0.018         0.126


           BETA
              I             S             X1            X2
              ________      ________      ________      ________
 I              0.000         0.000         1.000         0.500
 S              0.000         0.000         0.400         0.250
 X1             0.000         0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000


           PSI
              I             S             X1            X2
              ________      ________      ________      ________
 I              1.000
 S              0.100         0.200
 X1             0.000         0.000         0.880
 X2             0.000         0.000        -0.027         0.110


     POPULATION VALUES


           NU
              Y1            Y2            Y3            Y4            X1
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           NU
              X2
              ________
 1              0.000


           LAMBDA
              I             S             X1            X2
              ________      ________      ________      ________
 Y1             1.000         0.000         0.000         0.000
 Y2             1.000         1.000         0.000         0.000
 Y3             1.000         2.000         0.000         0.000
 Y4             1.000         3.000         0.000         0.000
 X1             0.000         0.000         1.000         0.000
 X2             0.000         0.000         0.000         1.000


           THETA
              Y1            Y2            Y3            Y4            X1
              ________      ________      ________      ________      ________
 Y1             0.500
 Y2             0.000         0.500
 Y3             0.000         0.000         0.500
 Y4             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


           THETA
              X2
              ________
 X2             0.000


           ALPHA
              I             S             X1            X2
              ________      ________      ________      ________
 1              1.000         2.000         0.000         0.000


           BETA
              I             S             X1            X2
              ________      ________      ________      ________
 I              0.000         0.000         1.000         0.500
 S              0.000         0.000         0.400         0.250
 X1             0.000         0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000


           PSI
              I             S             X1            X2
              ________      ________      ________      ________
 I              1.000
 S              0.100         0.200
 X1             0.000         0.000         1.000
 X2             0.000         0.000         0.000         1.000


TECHNICAL 9 OUTPUT

  Error messages for each replication (if any)



     Beginning Time:  17:44:04
        Ending Time:  17:44:06
       Elapsed Time:  00:00:02



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