```Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   4:39 AM

INPUT INSTRUCTIONS

TITLE:	this is an example of a Monte Carlo
simulation study where parameter estimates
saved from a real data analysis are used
for true population parameter values for
data generation and coverage
MONTECARLO:
NAMES ARE y1-y10 x1 x2;
NOBSERVATIONS = 500;
NREPS = 500;
SEED = 45335;
POPULATION = ex12.7estimates.dat;
COVERAGE = ex12.7estimates.dat;
MODEL POPULATION:
f1 BY y1-y5;
f2 BY y6-y10;
f1 ON x1 x2;
f2 ON x1 x2;
MODEL:	f1 BY y1-y5;
f2 BY y6-y10;
f1 ON x1 x2;
f2 ON x1 x2;
OUTPUT:	TECH9;

this is an example of a Monte Carlo
simulation study where parameter estimates
saved from a real data analysis are used
for true population parameter values for
data generation and coverage

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         500

Number of replications
Requested                                                  500
Completed                                                  500
Value of seed                                                45335

Number of dependent variables                                   10
Number of independent variables                                  2
Number of continuous latent variables                            2

Observed dependent variables

Continuous
Y1          Y2          Y3          Y4          Y5          Y6
Y7          Y8          Y9          Y10

Observed independent variables
X1          X2

Continuous latent variables
F1          F2

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
Y1            Y2            Y3            Y4            Y5
________      ________      ________      ________      ________
1.850         1.836         1.899         1.850         1.886

Means
Y6            Y7            Y8            Y9            Y10
________      ________      ________      ________      ________
2.851         2.807         2.878         2.856         2.872

Means
X1            X2
________      ________
1.070         1.006

Covariances
Y1            Y2            Y3            Y4            Y5
________      ________      ________      ________      ________
Y1             1.333
Y2             0.961         1.561
Y3             1.017         1.051         1.470
Y4             0.957         1.056         1.061         1.598
Y5             1.029         1.058         1.121         1.107         1.567
Y6             0.565         0.552         0.633         0.576         0.698
Y7             0.681         0.676         0.699         0.747         0.812
Y8             0.576         0.624         0.591         0.625         0.695
Y9             0.643         0.672         0.712         0.625         0.743
Y10            0.648         0.585         0.642         0.661         0.730
X1             0.464         0.478         0.490         0.464         0.568
X2             0.863         0.861         0.910         0.866         0.885

Covariances
Y6            Y7            Y8            Y9            Y10
________      ________      ________      ________      ________
Y6             1.685
Y7             1.076         1.955
Y8             0.864         1.168         1.650
Y9             1.084         1.256         1.072         2.006
Y10            0.908         1.127         0.959         1.137         1.638
X1             0.685         0.772         0.652         0.830         0.735
X2             0.426         0.614         0.494         0.476         0.505

Covariances
X1            X2
________      ________
X1             1.660
X2            -0.030         1.841

Correlations
Y1            Y2            Y3            Y4            Y5
________      ________      ________      ________      ________
Y1             1.000
Y2             0.666         1.000
Y3             0.726         0.693         1.000
Y4             0.655         0.668         0.692         1.000
Y5             0.712         0.676         0.739         0.700         1.000
Y6             0.377         0.341         0.402         0.351         0.429
Y7             0.422         0.387         0.412         0.423         0.464
Y8             0.388         0.389         0.380         0.385         0.432
Y9             0.393         0.380         0.414         0.349         0.419
Y10            0.439         0.366         0.414         0.409         0.455
X1             0.312         0.297         0.313         0.285         0.352
X2             0.551         0.508         0.553         0.505         0.521

Correlations
Y6            Y7            Y8            Y9            Y10
________      ________      ________      ________      ________
Y6             1.000
Y7             0.593         1.000
Y8             0.518         0.650         1.000
Y9             0.590         0.634         0.589         1.000
Y10            0.547         0.630         0.584         0.628         1.000
X1             0.410         0.428         0.394         0.455         0.446
X2             0.242         0.324         0.284         0.248         0.291

Correlations
X1            X2
________      ________
X1             1.000
X2            -0.017         1.000

MODEL FIT INFORMATION

Number of Free Parameters                       35

Loglikelihood

H0 Value

Mean                             -6570.990
Std Dev                             49.957
Number of successful computations      500

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.988        -6687.205      -6691.527
0.980       0.980        -6673.587      -6675.336
0.950       0.946        -6653.164      -6654.896
0.900       0.882        -6635.015      -6641.324
0.800       0.800        -6613.034      -6613.729
0.700       0.714        -6597.188      -6595.015
0.500       0.514        -6570.990      -6569.507
0.300       0.288        -6544.793      -6546.713
0.200       0.192        -6528.947      -6530.438
0.100       0.108        -6506.966      -6505.379
0.050       0.056        -6488.817      -6486.102
0.020       0.018        -6468.394      -6470.308
0.010       0.006        -6454.776      -6462.627

H1 Value

Mean                             -6545.782
Std Dev                             50.387
Number of successful computations      500

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.992        -6662.997      -6661.422
0.980       0.980        -6649.261      -6650.085
0.950       0.948        -6628.663      -6630.385
0.900       0.884        -6610.358      -6614.444
0.800       0.794        -6588.188      -6589.736
0.700       0.722        -6572.205      -6569.147
0.500       0.516        -6545.782      -6544.401
0.300       0.296        -6519.359      -6520.194
0.200       0.198        -6503.377      -6503.708
0.100       0.102        -6481.207      -6481.083
0.050       0.058        -6462.901      -6459.946
0.020       0.020        -6442.303      -6443.127
0.010       0.004        -6428.568      -6433.752

Information Criteria

Akaike (AIC)

Mean                             13211.981
Std Dev                             99.913
Number of successful computations      500

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.994        12979.552      12985.832
0.980       0.982        13006.789      13009.108
0.950       0.944        13047.633      13042.200
0.900       0.892        13083.932      13077.204
0.800       0.808        13127.894      13129.870
0.700       0.712        13159.586      13163.303
0.500       0.486        13211.981      13208.786
0.300       0.286        13264.376      13259.658
0.200       0.200        13296.068      13295.693
0.100       0.118        13340.030      13347.584
0.050       0.054        13376.329      13377.820
0.020       0.020        13417.173      13413.859
0.010       0.012        13444.410      13445.263

Bayesian (BIC)

Mean                             13359.492
Std Dev                             99.913
Number of successful computations      500

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.994        13127.064      13133.343
0.980       0.982        13154.300      13156.619
0.950       0.944        13195.145      13189.711
0.900       0.892        13231.443      13224.715
0.800       0.808        13275.405      13277.381
0.700       0.712        13307.098      13310.815
0.500       0.486        13359.492      13356.297
0.300       0.286        13411.887      13407.169
0.200       0.200        13443.579      13443.204
0.100       0.118        13487.541      13495.095
0.050       0.054        13523.840      13525.332
0.020       0.020        13564.685      13561.370
0.010       0.012        13591.921      13592.774

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

Mean                             13248.400
Std Dev                             99.913
Number of successful computations      500

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.994        13015.971      13022.251
0.980       0.982        13043.208      13045.527
0.950       0.944        13084.052      13078.619
0.900       0.892        13120.351      13113.623
0.800       0.808        13164.313      13166.289
0.700       0.712        13196.005      13199.722
0.500       0.486        13248.400      13245.205
0.300       0.286        13300.795      13296.077
0.200       0.200        13332.487      13332.112
0.100       0.118        13376.449      13384.003
0.050       0.054        13412.748      13414.240
0.020       0.020        13453.592      13450.278
0.010       0.012        13480.829      13481.682

Chi-Square Test of Model Fit

Degrees of freedom                      50

Mean                                50.417
Std Dev                             10.291
Number of successful computations      500

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.982           29.707         25.251
0.980       0.974           31.664         29.989
0.950       0.928           34.764         33.322
0.900       0.902           37.689         37.514
0.800       0.828           41.449         42.102
0.700       0.730           44.313         44.951
0.500       0.514           49.335         49.742
0.300       0.330           54.723         55.991
0.200       0.220           58.164         58.802
0.100       0.124           63.167         64.286
0.050       0.054           67.505         67.591
0.020       0.018           72.613         71.647
0.010       0.012           76.154         76.267

RMSEA (Root Mean Square Error Of Approximation)

Mean                                 0.008
Std Dev                              0.010
Number of successful computations      500

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       1.000           -0.015          0.000
0.980       1.000           -0.012          0.000
0.950       1.000           -0.008          0.000
0.900       1.000           -0.004          0.000
0.800       0.490            0.000          0.000
0.700       0.474            0.003          0.000
0.500       0.424            0.008          0.000
0.300       0.332            0.014          0.015
0.200       0.250            0.017          0.019
0.100       0.144            0.021          0.024
0.050       0.086            0.025          0.027
0.020       0.022            0.029          0.029
0.010       0.014            0.032          0.032

SRMR (Standardized Root Mean Square Residual)

Mean                                 0.017
Std Dev                              0.002
Number of successful computations      500

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.996            0.011          0.012
0.980       0.994            0.012          0.012
0.950       0.964            0.013          0.013
0.900       0.916            0.013          0.014
0.800       0.814            0.015          0.015
0.700       0.682            0.015          0.015
0.500       0.468            0.017          0.016
0.300       0.262            0.018          0.018
0.200       0.194            0.019          0.019
0.100       0.098            0.020          0.020
0.050       0.068            0.021          0.021
0.020       0.034            0.022          0.023
0.010       0.024            0.022          0.023

MODEL RESULTS

ESTIMATES              S. E.     M. S. E.  95%  % Sig
Population   Average   Std. Dev.   Average             Cover Coeff
F1       BY
Y1                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
Y2                  1.074     1.0756     0.0548     0.0520     0.0030 0.946 1.000
Y3                  1.113     1.1162     0.0507     0.0501     0.0026 0.950 1.000
Y4                  1.059     1.0637     0.0519     0.0515     0.0027 0.968 1.000
Y5                  1.067     1.0709     0.0518     0.0500     0.0027 0.942 1.000

F2       BY
Y6                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
Y7                  1.081     1.0873     0.0577     0.0571     0.0034 0.938 1.000
Y8                  0.943     0.9474     0.0551     0.0541     0.0030 0.948 1.000
Y9                  1.047     1.0524     0.0601     0.0570     0.0036 0.930 1.000
Y10                 1.008     1.0132     0.0561     0.0553     0.0032 0.948 1.000

F1       ON
X1                  0.262     0.2616     0.0241     0.0233     0.0006 0.936 1.000
X2                  0.459     0.4579     0.0282     0.0277     0.0008 0.950 1.000

F2       ON
X1                  0.482     0.4802     0.0317     0.0312     0.0010 0.932 1.000
X2                  0.295     0.2933     0.0306     0.0302     0.0009 0.944 1.000

F2       WITH
F1                  0.205     0.2019     0.0291     0.0288     0.0009 0.930 1.000

Intercepts
Y1                  1.097     1.0971     0.0604     0.0583     0.0036 0.938 1.000
Y2                  1.004     1.0033     0.0636     0.0625     0.0040 0.950 1.000
Y3                  0.999     1.0002     0.0628     0.0604     0.0039 0.942 1.000
Y4                  1.059     1.0564     0.0638     0.0619     0.0041 0.950 1.000
Y5                  1.092     1.0916     0.0631     0.0601     0.0040 0.946 1.000
Y6                  1.991     1.9951     0.0710     0.0713     0.0050 0.944 1.000
Y7                  1.912     1.9141     0.0770     0.0718     0.0059 0.934 1.000
Y8                  2.079     2.0798     0.0693     0.0685     0.0048 0.948 1.000
Y9                  1.961     1.9588     0.0768     0.0720     0.0059 0.938 1.000
Y10                 2.013     2.0130     0.0693     0.0698     0.0048 0.962 1.000

Residual Variances
Y1                  0.469     0.4662     0.0361     0.0350     0.0013 0.936 1.000
Y2                  0.535     0.5356     0.0397     0.0403     0.0016 0.938 1.000
Y3                  0.410     0.4091     0.0298     0.0334     0.0009 0.978 1.000
Y4                  0.529     0.5272     0.0383     0.0396     0.0015 0.952 1.000
Y5                  0.458     0.4538     0.0349     0.0353     0.0012 0.962 1.000
Y6                  0.794     0.7890     0.0590     0.0589     0.0035 0.946 1.000
Y7                  0.675     0.6739     0.0515     0.0540     0.0026 0.960 1.000
Y8                  0.749     0.7507     0.0531     0.0554     0.0028 0.964 1.000
Y9                  0.744     0.7395     0.0568     0.0570     0.0032 0.950 1.000
Y10                 0.712     0.7076     0.0555     0.0542     0.0031 0.942 1.000
F1                  0.407     0.3999     0.0417     0.0394     0.0018 0.918 1.000
F2                  0.546     0.5416     0.0612     0.0582     0.0038 0.928 1.000

QUALITY OF NUMERICAL RESULTS

Average Condition Number for the Information Matrix      0.783E-02
(ratio of smallest to largest eigenvalue)

TECHNICAL OUTPUT

PARAMETER SPECIFICATION

NU
Y1            Y2            Y3            Y4            Y5
________      ________      ________      ________      ________
1             2             3             4             5

NU
Y6            Y7            Y8            Y9            Y10
________      ________      ________      ________      ________
6             7             8             9            10

NU
X1            X2
________      ________
0             0

LAMBDA
F1            F2            X1            X2
________      ________      ________      ________
Y1                 0             0             0             0
Y2                11             0             0             0
Y3                12             0             0             0
Y4                13             0             0             0
Y5                14             0             0             0
Y6                 0             0             0             0
Y7                 0            15             0             0
Y8                 0            16             0             0
Y9                 0            17             0             0
Y10                0            18             0             0
X1                 0             0             0             0
X2                 0             0             0             0

THETA
Y1            Y2            Y3            Y4            Y5
________      ________      ________      ________      ________
Y1                19
Y2                 0            20
Y3                 0             0            21
Y4                 0             0             0            22
Y5                 0             0             0             0            23
Y6                 0             0             0             0             0
Y7                 0             0             0             0             0
Y8                 0             0             0             0             0
Y9                 0             0             0             0             0
Y10                0             0             0             0             0
X1                 0             0             0             0             0
X2                 0             0             0             0             0

THETA
Y6            Y7            Y8            Y9            Y10
________      ________      ________      ________      ________
Y6                24
Y7                 0            25
Y8                 0             0            26
Y9                 0             0             0            27
Y10                0             0             0             0            28
X1                 0             0             0             0             0
X2                 0             0             0             0             0

THETA
X1            X2
________      ________
X1                 0
X2                 0             0

ALPHA
F1            F2            X1            X2
________      ________      ________      ________
0             0             0             0

BETA
F1            F2            X1            X2
________      ________      ________      ________
F1                 0             0            29            30
F2                 0             0            31            32
X1                 0             0             0             0
X2                 0             0             0             0

PSI
F1            F2            X1            X2
________      ________      ________      ________
F1                33
F2                34            35
X1                 0             0             0
X2                 0             0             0             0

STARTING VALUES

NU
Y1            Y2            Y3            Y4            Y5
________      ________      ________      ________      ________
0.000         0.000         0.000         0.000         0.000

NU
Y6            Y7            Y8            Y9            Y10
________      ________      ________      ________      ________
0.000         0.000         0.000         0.000         0.000

NU
X1            X2
________      ________
0.000         0.000

LAMBDA
F1            F2            X1            X2
________      ________      ________      ________
Y1             1.000         0.000         0.000         0.000
Y2             1.045         0.000         0.000         0.000
Y3             1.095         0.000         0.000         0.000
Y4             1.068         0.000         0.000         0.000
Y5             1.115         0.000         0.000         0.000
Y6             0.000         1.000         0.000         0.000
Y7             0.000         1.227         0.000         0.000
Y8             0.000         1.042         0.000         0.000
Y9             0.000         1.209         0.000         0.000
Y10            0.000         1.058         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            Y5
________      ________      ________      ________      ________
Y1             0.500
Y2             0.000         0.500
Y3             0.000         0.000         0.500
Y4             0.000         0.000         0.000         0.500
Y5             0.000         0.000         0.000         0.000         0.500
Y6             0.000         0.000         0.000         0.000         0.000
Y7             0.000         0.000         0.000         0.000         0.000
Y8             0.000         0.000         0.000         0.000         0.000
Y9             0.000         0.000         0.000         0.000         0.000
Y10            0.000         0.000         0.000         0.000         0.000
X1             0.000         0.000         0.000         0.000         0.000
X2             0.000         0.000         0.000         0.000         0.000

THETA
Y6            Y7            Y8            Y9            Y10
________      ________      ________      ________      ________
Y6             0.500
Y7             0.000         0.500
Y8             0.000         0.000         0.500
Y9             0.000         0.000         0.000         0.500
Y10            0.000         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
X1            X2
________      ________
X1             0.000
X2             0.000         0.000

ALPHA
F1            F2            X1            X2
________      ________      ________      ________
0.000         0.000         1.070         1.006

BETA
F1            F2            X1            X2
________      ________      ________      ________
F1             0.000         0.000         0.000         0.000
F2             0.000         0.000         0.000         0.000
X1             0.000         0.000         0.000         0.000
X2             0.000         0.000         0.000         0.000

PSI
F1            F2            X1            X2
________      ________      ________      ________
F1             0.050
F2             0.000         0.050
X1             0.000         0.000         1.660
X2             0.000         0.000        -0.030         1.841

POPULATION VALUES

NU
Y1            Y2            Y3            Y4            Y5
________      ________      ________      ________      ________
1.097         1.004         0.999         1.059         1.092

NU
Y6            Y7            Y8            Y9            Y10
________      ________      ________      ________      ________
1.991         1.912         2.079         1.961         2.013

NU
X1            X2
________      ________
0.000         0.000

LAMBDA
F1            F2            X1            X2
________      ________      ________      ________
Y1             1.000         0.000         0.000         0.000
Y2             1.074         0.000         0.000         0.000
Y3             1.113         0.000         0.000         0.000
Y4             1.059         0.000         0.000         0.000
Y5             1.067         0.000         0.000         0.000
Y6             0.000         1.000         0.000         0.000
Y7             0.000         1.081         0.000         0.000
Y8             0.000         0.943         0.000         0.000
Y9             0.000         1.047         0.000         0.000
Y10            0.000         1.008         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            Y5
________      ________      ________      ________      ________
Y1             0.469
Y2             0.000         0.535
Y3             0.000         0.000         0.410
Y4             0.000         0.000         0.000         0.529
Y5             0.000         0.000         0.000         0.000         0.458
Y6             0.000         0.000         0.000         0.000         0.000
Y7             0.000         0.000         0.000         0.000         0.000
Y8             0.000         0.000         0.000         0.000         0.000
Y9             0.000         0.000         0.000         0.000         0.000
Y10            0.000         0.000         0.000         0.000         0.000
X1             0.000         0.000         0.000         0.000         0.000
X2             0.000         0.000         0.000         0.000         0.000

THETA
Y6            Y7            Y8            Y9            Y10
________      ________      ________      ________      ________
Y6             0.794
Y7             0.000         0.675
Y8             0.000         0.000         0.749
Y9             0.000         0.000         0.000         0.744
Y10            0.000         0.000         0.000         0.000         0.712
X1             0.000         0.000         0.000         0.000         0.000
X2             0.000         0.000         0.000         0.000         0.000

THETA
X1            X2
________      ________
X1             0.000
X2             0.000         0.000

ALPHA
F1            F2            X1            X2
________      ________      ________      ________
0.000         0.000         1.023         1.042

BETA
F1            F2            X1            X2
________      ________      ________      ________
F1             0.000         0.000         0.262         0.459
F2             0.000         0.000         0.482         0.295
X1             0.000         0.000         0.000         0.000
X2             0.000         0.000         0.000         0.000

PSI
F1            F2            X1            X2
________      ________      ________      ________
F1             0.407
F2             0.205         0.546
X1             0.000         0.000         2.030
X2             0.000         0.000        -0.021         1.719

TECHNICAL 9 OUTPUT

Error messages for each replication (if any)

Beginning Time:  04:39:18
Ending Time:  04:39:21
Elapsed Time:  00:00:03

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