Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:08 PM
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;
INPUT READING TERMINATED NORMALLY
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
Cumulative Distribution Function
Value Function Value
0.990 1.000
0.980 1.000
0.950 1.000
0.900 1.000
0.800 1.000
0.700 1.000
0.500 1.000
0.300 1.000
0.200 1.000
0.100 1.000
0.050 1.000
0.020 0.830
0.010 0.592
CFI/TLI
CFI
Mean 0.999
Std Dev 0.002
Number of successful computations 500
Cumulative Distribution Function
Value Function Value
0.990 0.000
0.980 0.000
0.950 0.000
0.900 0.000
0.800 0.000
0.700 0.000
0.500 0.000
0.300 0.000
0.200 0.000
0.100 0.000
0.050 0.000
0.020 0.000
0.010 0.000
TLI
Mean 0.998
Std Dev 0.002
Number of successful computations 500
Cumulative Distribution Function
Value Function Value
0.990 0.000
0.980 0.000
0.950 0.000
0.900 0.000
0.800 0.000
0.700 0.000
0.500 0.000
0.300 0.000
0.200 0.000
0.100 0.000
0.050 0.000
0.020 0.000
0.010 0.000
SRMR (Standardized Root Mean Square Residual)
Mean 0.017
Std Dev 0.003
Number of successful computations 500
Cumulative Distribution Function
Value Function Value
0.990 1.000
0.980 1.000
0.950 1.000
0.900 1.000
0.800 1.000
0.700 1.000
0.500 1.000
0.300 1.000
0.200 1.000
0.100 1.000
0.050 1.000
0.020 0.882
0.010 0.002
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: 23:08:54
Ending Time: 23:08:58
Elapsed Time: 00:00:04
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