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 two-level
mediation model with random slopes
MONTECARLO:
NAMES ARE y m x;
WITHIN = x;
NOBSERVATIONS = 1000;
NCSIZES = 1;
CSIZES = 100 (10);
NREP = 100;
ANALYSIS: TYPE = TWOLEVEL RANDOM;
MODEL POPULATION:
%WITHIN%
x@1;
c | y ON x;
b | y ON m;
a | m ON x;
m*1; y*1;
%BETWEEN%
y WITH m*0.1 b*0.1 a*0.1 c*0.1;
m WITH b*0.1 a*0.1 c*0.1;
a WITH b*0.1 (cab);
a WITH c*0.1;
b WITH c*0.1;
y*1 m*1 a*1 b*1 c*1;
[a*0.4] (ma);
[b*0.5] (mb);
[c*0.6];
MODEL:
%WITHIN%
c | y ON x;
b | y ON m;
a | m ON x;
m*1; y*1;
%BETWEEN%
y WITH m*0.1 b*0.1 a*0.1 c*0.1;
m WITH b*0.1 a*0.1 c*0.1;
a WITH b*0.1 (cab);
a WITH c*0.1;
b WITH c*0.1;
y*1 m*1 a*1 b*1 c*1;
[a*0.4] (ma);
[b*0.5] (mb);
[c*0.6];
MODEL CONSTRAINT:
NEW(m*0.3);
m=ma*mb+cab;
*** WARNING in MODEL command
In the MODEL command, the predictor variable on the WITHIN level refers to the whole observed
variable. To use the latent within-level part, use ESTIMATOR=BAYES in the ANALYSIS command.
This applies to the following statement(s):
B | Y ON M
*** WARNING in MODEL POPULATION command
In the MODEL POPULATION command, the predictor variable on the WITHIN level refers to the whole observed
variable. To use the latent within-level part, use ESTIMATOR=BAYES in the ANALYSIS command.
This applies to the following statement(s):
B | Y ON M
2 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
this is an example of a Monte Carlo simulation study for a two-level
mediation model with random slopes
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 1000
Number of replications
Requested 100
Completed 100
Value of seed 0
Number of dependent variables 2
Number of independent variables 1
Number of continuous latent variables 3
Observed dependent variables
Continuous
Y M
Observed independent variables
X
Continuous latent variables
C B A
Variables with special functions
Within variables
X
Estimator MLR
Information matrix OBSERVED
Maximum number of iterations 100
Convergence criterion 0.100D-05
Maximum number of EM iterations 500
Convergence criteria for the EM algorithm
Loglikelihood change 0.100D-02
Relative loglikelihood change 0.100D-05
Derivative 0.100D-03
Minimum variance 0.100D-03
Maximum number of steepest descent iterations 20
Maximum number of iterations for H1 2000
Convergence criterion for H1 0.100D-03
Optimization algorithm EMA
SUMMARY OF DATA FOR THE FIRST REPLICATION
Cluster information
Size (s) Number of clusters of Size s
10 100
Average cluster size 10.000
Estimated Intraclass Correlations for the Y Variables
Intraclass Intraclass Intraclass
Variable Correlation Variable Correlation Variable Correlation
Y 0.324 M 0.329
SAMPLE STATISTICS FOR THE FIRST REPLICATION
NOTE: The sample statistics for within and between refer to the
maximum-likelihood estimated within and between covariance
matrices, respectively.
ESTIMATED SAMPLE STATISTICS FOR WITHIN
Means
Y M X
________ ________ ________
0.000 0.000 -0.010
Covariances
Y M X
________ ________ ________
Y 4.973
M 1.237 2.198
X 0.823 0.376 1.053
Correlations
Y M X
________ ________ ________
Y 1.000
M 0.374 1.000
X 0.360 0.247 1.000
ESTIMATED SAMPLE STATISTICS FOR BETWEEN
Means
Y M X
________ ________ ________
-0.225 0.059 0.000
Covariances
Y M X
________ ________ ________
Y 2.386
M 0.512 1.076
X 0.000 0.000 0.000
Correlations
Y M X
________ ________ ________
Y 1.000
M 0.319 1.000
X 0.000 0.000 0.000
MODEL FIT INFORMATION
Number of Free Parameters 22
Loglikelihood
H0 Value
Mean -3406.247
Std Dev 33.122
Number of successful computations 100
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.980 -3483.298 -3503.374
0.980 0.980 -3474.269 -3496.144
0.950 0.940 -3460.729 -3467.424
0.900 0.890 -3448.696 -3449.629
0.800 0.790 -3434.122 -3438.313
0.700 0.690 -3423.616 -3424.433
0.500 0.540 -3406.247 -3401.548
0.300 0.280 -3388.878 -3389.968
0.200 0.180 -3378.372 -3380.798
0.100 0.100 -3363.798 -3368.446
0.050 0.020 -3351.765 -3353.512
0.020 0.010 -3338.225 -3352.682
0.010 0.010 -3329.196 -3350.233
Information Criteria
Akaike (AIC)
Mean 6856.494
Std Dev 66.244
Number of successful computations 100
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.990 6702.392 6661.895
0.980 0.990 6720.450 6744.466
0.950 0.980 6747.530 6750.930
0.900 0.900 6771.596 6770.412
0.800 0.820 6800.743 6804.722
0.700 0.720 6821.756 6823.575
0.500 0.460 6856.494 6845.770
0.300 0.310 6891.232 6892.209
0.200 0.210 6912.244 6913.247
0.100 0.110 6941.392 6941.687
0.050 0.060 6965.458 6965.866
0.020 0.020 6992.538 6987.019
0.010 0.020 7010.596 7036.289
Bayesian (BIC)
Mean 6964.464
Std Dev 66.244
Number of successful computations 100
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.990 6810.362 6769.866
0.980 0.990 6828.420 6852.437
0.950 0.980 6855.500 6858.901
0.900 0.900 6879.567 6878.383
0.800 0.820 6908.714 6912.692
0.700 0.720 6929.726 6931.546
0.500 0.460 6964.464 6953.741
0.300 0.310 6999.203 7000.180
0.200 0.210 7020.215 7021.218
0.100 0.110 7049.362 7049.658
0.050 0.060 7073.428 7073.837
0.020 0.020 7100.509 7094.989
0.010 0.020 7118.567 7144.259
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 6894.591
Std Dev 66.244
Number of successful computations 100
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.990 6740.489 6699.992
0.980 0.990 6758.547 6782.564
0.950 0.980 6785.627 6789.028
0.900 0.900 6809.694 6808.510
0.800 0.820 6838.841 6842.819
0.700 0.720 6859.853 6861.672
0.500 0.460 6894.591 6883.868
0.300 0.310 6929.329 6930.306
0.200 0.210 6950.342 6951.345
0.100 0.110 6979.489 6979.784
0.050 0.060 7003.555 7003.964
0.020 0.020 7030.636 7025.116
0.010 0.020 7048.694 7074.386
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Within Level
Residual Variances
Y 1.000 1.0020 0.0531 0.0530 0.0028 0.960 1.000
M 1.000 1.0011 0.0538 0.0496 0.0029 0.910 1.000
Between Level
Y WITH
B 0.100 0.1212 0.1247 0.1140 0.0158 0.910 0.210
A 0.100 0.1087 0.1318 0.1162 0.0173 0.910 0.190
C 0.100 0.0868 0.1123 0.1237 0.0127 0.940 0.090
M WITH
B 0.100 0.1033 0.1029 0.1085 0.0105 0.940 0.120
A 0.100 0.0815 0.1081 0.1116 0.0119 0.950 0.070
C 0.100 0.1138 0.1148 0.1165 0.0132 0.970 0.160
A WITH
B 0.100 0.0965 0.1174 0.1101 0.0137 0.920 0.150
C 0.100 0.0755 0.1380 0.1312 0.0194 0.910 0.110
B WITH
C 0.100 0.0892 0.1056 0.1156 0.0112 0.960 0.070
Y WITH
M 0.100 0.1034 0.1344 0.1284 0.0179 0.940 0.140
Means
Y 0.000 0.0070 0.1151 0.1113 0.0132 0.950 0.050
M 0.000 -0.0031 0.1102 0.1056 0.0120 0.950 0.050
C 0.600 0.5979 0.1230 0.1125 0.0150 0.930 1.000
B 0.500 0.5022 0.1280 0.1061 0.0162 0.890 1.000
A 0.400 0.3854 0.0972 0.1072 0.0096 0.970 0.970
Variances
Y 1.000 1.0071 0.1682 0.1689 0.0281 0.910 1.000
M 1.000 1.0113 0.1782 0.1571 0.0316 0.930 1.000
C 1.000 0.9801 0.1414 0.1717 0.0202 0.980 1.000
B 1.000 0.9768 0.1443 0.1545 0.0212 0.950 1.000
A 1.000 1.0188 0.1541 0.1587 0.0239 0.950 1.000
New/Additional Parameters
M 0.300 0.2904 0.1423 0.1315 0.0201 0.950 0.550
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.144E-02
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
NU
Y M X
________ ________ ________
0 0 0
LAMBDA
Y M X
________ ________ ________
Y 0 0 0
M 0 0 0
X 0 0 0
THETA
Y M X
________ ________ ________
Y 0
M 0 0
X 0 0 0
ALPHA
Y M X
________ ________ ________
0 0 0
BETA
Y M X
________ ________ ________
Y 0 0 0
M 0 0 0
X 0 0 0
PSI
Y M X
________ ________ ________
Y 1
M 0 2
X 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN
NU
Y M
________ ________
0 0
LAMBDA
C B A Y M
________ ________ ________ ________ ________
Y 0 0 0 0 0
M 0 0 0 0 0
THETA
Y M
________ ________
Y 0
M 0 0
ALPHA
C B A Y M
________ ________ ________ ________ ________
3 4 5 6 7
BETA
C B A Y M
________ ________ ________ ________ ________
C 0 0 0 0 0
B 0 0 0 0 0
A 0 0 0 0 0
Y 0 0 0 0 0
M 0 0 0 0 0
PSI
C B A Y M
________ ________ ________ ________ ________
C 8
B 9 10
A 11 12 13
Y 14 15 16 17
M 18 19 20 21 22
PARAMETER SPECIFICATION FOR THE ADDITIONAL PARAMETERS
NEW/ADDITIONAL PARAMETERS
M
________
23
STARTING VALUES FOR WITHIN
NU
Y M X
________ ________ ________
0.000 0.000 0.000
LAMBDA
Y M X
________ ________ ________
Y 1.000 0.000 0.000
M 0.000 1.000 0.000
X 0.000 0.000 1.000
THETA
Y M X
________ ________ ________
Y 0.000
M 0.000 0.000
X 0.000 0.000 0.000
ALPHA
Y M X
________ ________ ________
0.000 0.000 0.000
BETA
Y M X
________ ________ ________
Y 0.000 0.000 0.000
M 0.000 0.000 0.000
X 0.000 0.000 0.000
PSI
Y M X
________ ________ ________
Y 1.000
M 0.000 1.000
X 0.000 0.000 0.500
STARTING VALUES FOR BETWEEN
NU
Y M
________ ________
0.000 0.000
LAMBDA
C B A Y M
________ ________ ________ ________ ________
Y 0.000 0.000 0.000 1.000 0.000
M 0.000 0.000 0.000 0.000 1.000
THETA
Y M
________ ________
Y 0.000
M 0.000 0.000
ALPHA
C B A Y M
________ ________ ________ ________ ________
0.600 0.500 0.400 0.000 0.000
BETA
C B A Y M
________ ________ ________ ________ ________
C 0.000 0.000 0.000 0.000 0.000
B 0.000 0.000 0.000 0.000 0.000
A 0.000 0.000 0.000 0.000 0.000
Y 0.000 0.000 0.000 0.000 0.000
M 0.000 0.000 0.000 0.000 0.000
PSI
C B A Y M
________ ________ ________ ________ ________
C 1.000
B 0.100 1.000
A 0.100 0.100 1.000
Y 0.100 0.100 0.100 1.000
M 0.100 0.100 0.100 0.100 1.000
STARTING VALUES FOR THE ADDITIONAL PARAMETERS
NEW/ADDITIONAL PARAMETERS
M
________
0.300
POPULATION VALUES FOR WITHIN
NU
Y M X
________ ________ ________
0.000 0.000 0.000
LAMBDA
Y M X
________ ________ ________
Y 1.000 0.000 0.000
M 0.000 1.000 0.000
X 0.000 0.000 1.000
THETA
Y M X
________ ________ ________
Y 0.000
M 0.000 0.000
X 0.000 0.000 0.000
ALPHA
Y M X
________ ________ ________
0.000 0.000 0.000
BETA
Y M X
________ ________ ________
Y 0.000 0.000 0.000
M 0.000 0.000 0.000
X 0.000 0.000 0.000
PSI
Y M X
________ ________ ________
Y 1.000
M 0.000 1.000
X 0.000 0.000 1.000
POPULATION VALUES FOR BETWEEN
NU
Y M
________ ________
0.000 0.000
LAMBDA
C B A Y M
________ ________ ________ ________ ________
Y 0.000 0.000 0.000 1.000 0.000
M 0.000 0.000 0.000 0.000 1.000
THETA
Y M
________ ________
Y 0.000
M 0.000 0.000
ALPHA
C B A Y M
________ ________ ________ ________ ________
0.600 0.500 0.400 0.000 0.000
BETA
C B A Y M
________ ________ ________ ________ ________
C 0.000 0.000 0.000 0.000 0.000
B 0.000 0.000 0.000 0.000 0.000
A 0.000 0.000 0.000 0.000 0.000
Y 0.000 0.000 0.000 0.000 0.000
M 0.000 0.000 0.000 0.000 0.000
PSI
C B A Y M
________ ________ ________ ________ ________
C 1.000
B 0.100 1.000
A 0.100 0.100 1.000
Y 0.100 0.100 0.100 1.000
M 0.100 0.100 0.100 0.100 1.000
Beginning Time: 23:06:23
Ending Time: 23:06:25
Elapsed Time: 00:00:02
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