Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:05 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
________ ________ ________ ________ ________
0.150 0.064 0.002 0.091 0.028
Means
X2
________
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
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 0.974
0.020 0.724
0.010 0.626
CFI/TLI
CFI
Mean 0.999
Std Dev 0.002
Number of successful computations 500
Cumulative Distribution Function
Value Function Value
0.990 0.012
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 0.004
Number of successful computations 500
Cumulative Distribution Function
Value Function Value
0.990 0.076
0.980 0.006
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 0.028
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 0.000
0.010 0.000
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 2 3 4 0
NU
X2
________
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
________ ________ ________
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
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
X2
________
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
________ ________ ________
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
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
X2
________
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
________ ________ ________
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: 23:05:59
Ending Time: 23:06:02
Elapsed Time: 00:00:03
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