Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:06 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
________ ________ ________ ________ ________
1.110 3.078 5.038 7.107 -0.018
Means
X2
________
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
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 0.968
0.020 0.680
0.010 0.586
CFI/TLI
CFI
Mean 0.999
Std Dev 0.002
Number of successful computations 500
Cumulative Distribution Function
Value Function Value
0.990 0.006
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 0.003
Number of successful computations 500
Cumulative Distribution Function
Value Function Value
0.990 0.040
0.980 0.004
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 0.016
Std Dev 0.006
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 0.772
0.010 0.106
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
________ ________ ________ ________ ________
0 0 0 0 0
NU
X2
________
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
________ ________ ________ ________
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
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
X2
________
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
________ ________ ________ ________
1.000 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
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
X2
________
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
________ ________ ________ ________
1.000 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: 23:06:26
Ending Time: 23:06:30
Elapsed Time: 00:00:04
MUTHEN & MUTHEN
3463 Stoner Ave.
Los Angeles, CA 90066
Tel: (310) 391-9971
Fax: (310) 391-8971
Web: www.StatModel.com
Support: Support@StatModel.com
Copyright (c) 1998-2022 Muthen & Muthen