Mplus VERSION 7
MUTHEN & MUTHEN
09/22/2012  10:47 PM

INPUT INSTRUCTIONS

  TITLE:	this is an example of a Monte Carlo
  	simulation study for a CFA with covariates
  	(MIMIC) with continuous factor indicators
  	and patterns of missing data
  MONTECARLO:
  	NAMES ARE y1-y4 x1 x2;
  	NOBSERVATIONS = 500;
  	NREPS = 500;
  	SEED = 4533;
  	CUTPOINTS = x2(1);
  	PATMISS = y1(.1) y2(.2) y3(.3) y4(1) |
  	          y1(1) y2(.1) y3(.2) y4(.3);
  	PATPROBS = .4 | .6;
  MODEL POPULATION:
  	[x1-x2@0];	
  	x1-x2@1;
  	f BY y1@1 y2-y4*1;
  	f*.5;
  	y1-y4*.5;
  	f ON x1*1 x2*.3;
  MODEL:	f BY y1@1 y2-y4*1;
  	f*.5;
  	y1-y4*.5;
  	f ON x1*1 x2*.3;
  OUTPUT:	TECH9;



INPUT READING TERMINATED NORMALLY



this is an example of a Monte Carlo
simulation study for a CFA with covariates
(MIMIC) with continuous factor indicators
and patterns of missing data

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                            1

Observed dependent variables

  Continuous
   Y1          Y2          Y3          Y4

Observed independent variables
   X1          X2

Continuous latent variables
   F


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            11


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
 Y1        x  x  x  x  x
 Y2        x  x  x        x  x  x  x
 Y3        x  x     x     x  x        x  x
 Y4        x              x     x     x     x
 X1        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


     MISSING DATA PATTERN FREQUENCIES

    Pattern   Frequency     Pattern   Frequency     Pattern   Frequency
          1           0           5          15           9          28
          2          86           6         143          10          25
          3          43           7          72          11          10
          4          34           8          39          12           5


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             0.356
 Y2             0.258         0.822
 Y3             0.240         0.602         0.740
 Y4             0.000         0.364         0.336         0.424
 X1             0.356         0.822         0.740         0.424         1.000
 X2             0.356         0.822         0.740         0.424         1.000


           Covariance Coverage
              X2
              ________
 X2             1.000



SAMPLE STATISTICS FOR THE FIRST REPLICATION


     ESTIMATED SAMPLE STATISTICS


           Means
              Y1            Y2            Y3            Y4            X1
              ________      ________      ________      ________      ________
      1         0.150         0.064         0.002         0.091         0.028


           Means
              X2
              ________
      1         0.134


           Covariances
              Y1            Y2            Y3            Y4            X1
              ________      ________      ________      ________      ________
 Y1             1.913
 Y2             1.425         2.045
 Y3             1.569         1.501         2.002
 Y4             1.257         1.530         1.471         2.001
 X1             0.944         0.919         0.966         0.906         0.933
 X2            -0.019        -0.011        -0.010         0.015        -0.024


           Covariances
              X2
              ________
 X2             0.116


           Correlations
              Y1            Y2            Y3            Y4            X1
              ________      ________      ________      ________      ________
 Y1             1.000
 Y2             0.720         1.000
 Y3             0.802         0.742         1.000
 Y4             0.643         0.756         0.735         1.000
 X1             0.707         0.666         0.707         0.663         1.000
 X2            -0.041        -0.022        -0.021         0.031        -0.072


           Correlations
              X2
              ________
 X2             1.000


     MAXIMUM LOG-LIKELIHOOD VALUE FOR THE UNRESTRICTED (H1) MODEL IS   -2430.567


MODEL FIT INFORMATION

Number of Free Parameters                       14

Loglikelihood

    H0 Value

        Mean                             -1588.257
        Std Dev                             29.720
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.994        -1657.394      -1649.842
           0.980       0.990        -1649.292      -1645.515
           0.950       0.946        -1637.143      -1637.920
           0.900       0.884        -1626.346      -1628.470
           0.800       0.784        -1613.269      -1615.842
           0.700       0.708        -1603.842      -1603.504
           0.500       0.510        -1588.257      -1587.526
           0.300       0.288        -1572.672      -1573.872
           0.200       0.190        -1563.244      -1563.785
           0.100       0.102        -1550.168      -1549.953
           0.050       0.058        -1539.370      -1536.887
           0.020       0.024        -1527.221      -1523.431
           0.010       0.014        -1519.119      -1516.108

    H1 Value

        Mean                             -1584.813
        Std Dev                             29.793
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.994        -1654.121      -1648.054
           0.980       0.990        -1645.999      -1643.079
           0.950       0.948        -1633.820      -1635.016
           0.900       0.886        -1622.996      -1625.639
           0.800       0.784        -1609.887      -1611.365
           0.700       0.710        -1600.436      -1599.132
           0.500       0.520        -1584.813      -1583.911
           0.300       0.290        -1569.189      -1569.747
           0.200       0.188        -1559.739      -1560.794
           0.100       0.102        -1546.630      -1546.474
           0.050       0.060        -1535.806      -1533.285
           0.020       0.024        -1523.626      -1520.275
           0.010       0.014        -1515.504      -1512.923

Information Criteria

    Akaike (AIC)

        Mean                              3204.513
        Std Dev                             59.440
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.986         3066.239       3059.535
           0.980       0.976         3082.442       3073.460
           0.950       0.942         3106.741       3099.604
           0.900       0.898         3128.335       3126.783
           0.800       0.810         3154.489       3155.214
           0.700       0.712         3173.343       3175.456
           0.500       0.490         3204.513       3202.438
           0.300       0.292         3235.684       3234.727
           0.200       0.216         3254.538       3256.451
           0.100       0.116         3280.691       3284.066
           0.050       0.054         3302.286       3302.777
           0.020       0.010         3326.585       3317.450
           0.010       0.006         3342.788       3323.753

    Bayesian (BIC)

        Mean                              3263.518
        Std Dev                             59.440
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.986         3125.243       3118.540
           0.980       0.976         3141.447       3132.464
           0.950       0.942         3165.745       3158.609
           0.900       0.898         3187.340       3185.788
           0.800       0.810         3213.493       3214.219
           0.700       0.712         3232.348       3234.461
           0.500       0.490         3263.518       3261.442
           0.300       0.292         3294.688       3293.732
           0.200       0.216         3313.542       3315.455
           0.100       0.116         3339.696       3343.070
           0.050       0.054         3361.290       3361.781
           0.020       0.010         3385.589       3376.455
           0.010       0.006         3401.793       3382.757

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

        Mean                              3219.081
        Std Dev                             59.440
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.986         3080.806       3074.103
           0.980       0.976         3097.010       3088.027
           0.950       0.942         3121.309       3114.172
           0.900       0.898         3142.903       3141.351
           0.800       0.810         3169.057       3169.782
           0.700       0.712         3187.911       3190.024
           0.500       0.490         3219.081       3217.006
           0.300       0.292         3250.251       3249.295
           0.200       0.216         3269.106       3271.019
           0.100       0.116         3295.259       3298.633
           0.050       0.054         3316.854       3317.345
           0.020       0.010         3341.153       3332.018
           0.010       0.006         3357.356       3338.320

Chi-Square Test of Model Fit

        Degrees of freedom                       7

        Mean                                 6.888
        Std Dev                              3.582
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.994            1.239          1.446
           0.980       0.980            1.564          1.562
           0.950       0.942            2.167          2.125
           0.900       0.896            2.833          2.676
           0.800       0.806            3.822          3.841
           0.700       0.720            4.671          4.791
           0.500       0.490            6.346          6.239
           0.300       0.280            8.383          8.090
           0.200       0.170            9.803          9.373
           0.100       0.106           12.017         12.073
           0.050       0.052           14.067         14.081
           0.020       0.016           16.622         16.278
           0.010       0.006           18.475         17.024

RMSEA (Root Mean Square Error Of Approximation)

        Mean                                 0.011
        Std Dev                              0.016
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       1.000           -0.026          0.000
           0.980       1.000           -0.022          0.000
           0.950       1.000           -0.015          0.000
           0.900       1.000           -0.009          0.000
           0.800       1.000           -0.002          0.000
           0.700       0.400            0.003          0.000
           0.500       0.368            0.011          0.000
           0.300       0.280            0.020          0.018
           0.200       0.210            0.025          0.026
           0.100       0.140            0.032          0.038
           0.050       0.112            0.038          0.045
           0.020       0.058            0.044          0.051
           0.010       0.028            0.049          0.054

SRMR (Standardized Root Mean Square Residual)

        Mean                                 0.025
        Std Dev                              0.003
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       1.000            0.018          0.020
           0.980       1.000            0.019          0.020
           0.950       0.974            0.020          0.021
           0.900       0.930            0.021          0.021
           0.800       0.788            0.023          0.022
           0.700       0.680            0.023          0.023
           0.500       0.486            0.025          0.025
           0.300       0.262            0.027          0.026
           0.200       0.166            0.027          0.027
           0.100       0.076            0.029          0.028
           0.050       0.058            0.030          0.030
           0.020       0.038            0.031          0.032
           0.010       0.020            0.032          0.034


MODEL RESULTS

                           ESTIMATES              S. E.     M. S. E.  95%  % Sig
              Population   Average   Std. Dev.   Average             Cover Coeff
 F        BY
  Y1               1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y2               1.000     1.0028     0.0663     0.0622     0.0044 0.940 1.000
  Y3               1.000     1.0005     0.0674     0.0633     0.0045 0.930 1.000
  Y4               1.000     1.0020     0.0806     0.0743     0.0065 0.932 1.000

 F        ON
  X1               1.000     1.0023     0.0670     0.0620     0.0045 0.938 1.000
  X2               0.300     0.2991     0.1065     0.1052     0.0113 0.958 0.810

 Intercepts
  Y1               0.000    -0.0018     0.0719     0.0688     0.0052 0.950 0.050
  Y2               0.000     0.0022     0.0515     0.0500     0.0027 0.946 0.054
  Y3               0.000     0.0015     0.0535     0.0519     0.0029 0.944 0.056
  Y4               0.000     0.0005     0.0604     0.0644     0.0036 0.962 0.038

 Residual Variances
  Y1               0.500     0.4887     0.0776     0.0779     0.0061 0.944 1.000
  Y2               0.500     0.4982     0.0502     0.0513     0.0025 0.950 1.000
  Y3               0.500     0.4966     0.0558     0.0532     0.0031 0.926 1.000
  Y4               0.500     0.4905     0.0755     0.0697     0.0058 0.920 1.000
  F                0.500     0.5019     0.0715     0.0679     0.0051 0.930 1.000


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.491E-01
       (ratio of smallest to largest eigenvalue)


TECHNICAL OUTPUT


     PARAMETER SPECIFICATION


           NU
              Y1            Y2            Y3            Y4            X1
              ________      ________      ________      ________      ________
      1           1             2             3             4             0


           NU
              X2
              ________
      1           0


           LAMBDA
              F             X1            X2
              ________      ________      ________
 Y1                 0             0             0
 Y2                 5             0             0
 Y3                 6             0             0
 Y4                 7             0             0
 X1                 0             0             0
 X2                 0             0             0


           THETA
              Y1            Y2            Y3            Y4            X1
              ________      ________      ________      ________      ________
 Y1                 8
 Y2                 0             9
 Y3                 0             0            10
 Y4                 0             0             0            11
 X1                 0             0             0             0             0
 X2                 0             0             0             0             0


           THETA
              X2
              ________
 X2                 0


           ALPHA
              F             X1            X2
              ________      ________      ________
      1           0             0             0


           BETA
              F             X1            X2
              ________      ________      ________
 F                  0            12            13
 X1                 0             0             0
 X2                 0             0             0


           PSI
              F             X1            X2
              ________      ________      ________
 F                 14
 X1                 0             0
 X2                 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
              F             X1            X2
              ________      ________      ________
 Y1             1.000         0.000         0.000
 Y2             0.986         0.000         0.000
 Y3             1.085         0.000         0.000
 Y4             0.978         0.000         0.000
 X1             0.000         1.000         0.000
 X2             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
              F             X1            X2
              ________      ________      ________
      1         0.000         0.028         0.134


           BETA
              F             X1            X2
              ________      ________      ________
 F              0.000         1.000         0.300
 X1             0.000         0.000         0.000
 X2             0.000         0.000         0.000


           PSI
              F             X1            X2
              ________      ________      ________
 F              0.500
 X1             0.000         0.933
 X2             0.000        -0.024         0.116


     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
              F             X1            X2
              ________      ________      ________
 Y1             1.000         0.000         0.000
 Y2             1.000         0.000         0.000
 Y3             1.000         0.000         0.000
 Y4             1.000         0.000         0.000
 X1             0.000         1.000         0.000
 X2             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
              F             X1            X2
              ________      ________      ________
 1              0.000         0.000         0.000


           BETA
              F             X1            X2
              ________      ________      ________
 F              0.000         1.000         0.300
 X1             0.000         0.000         0.000
 X2             0.000         0.000         0.000


           PSI
              F             X1            X2
              ________      ________      ________
 F              0.500
 X1             0.000         1.000
 X2             0.000         0.000         1.000


TECHNICAL 9 OUTPUT

  Error messages for each replication (if any)



     Beginning Time:  22:47:23
        Ending Time:  22:47:26
       Elapsed Time:  00:00:03



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