Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017 4:53 AM
INPUT INSTRUCTIONS
TITLE: this an example of a Monte Carlo simulation
for a three-level path analysis model with a
continuous and a categorical dependent variable
DATA: FILE = ex9.21.dat;
VARIABLE: NAMES = u y2 y y3 x w z level2 level3;
CATEGORICAL = u;
WITHIN = x;
BETWEEN = y2 (level2) w (level3) z y3;
CLUSTER = level3 level2;
ANALYSIS: TYPE = threelevel;
ESTIMATOR = BAYES;
PROCESSORS = 2;
BITERATIONS = (1000);
MODEL: %WITHIN%
u ON y x;
y ON x;
%BETWEEN level2%
u ON w y y2;
y ON w;
y2 ON w;
y WITH y2;
y; y2; u;
%BETWEEN level3%
u ON y y2;
y ON z;
y2 ON z;
y3 ON y y2;
y WITH y2;
y; y2; u; y3;
u WITH y3;
OUTPUT: TECH1 TECH8;
INPUT READING TERMINATED NORMALLY
this an example of a Monte Carlo simulation
for a three-level path analysis model with a
continuous and a categorical dependent variable
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 7500
Number of dependent variables 4
Number of independent variables 3
Number of continuous latent variables 0
Observed dependent variables
Continuous
Y2 Y Y3
Binary and ordered categorical (ordinal)
U
Observed independent variables
X W Z
Variables with special functions
Cluster variables LEVEL3 LEVEL2
Within variables
X
Level 2 between variables
W
Level 3 between variables
Z Y3
Level 2 and level 3 between variables
Y2
Estimator BAYES
Specifications for Bayesian Estimation
Point estimate MEDIAN
Number of Markov chain Monte Carlo (MCMC) chains 2
Random seed for the first chain 0
Starting value information UNPERTURBED
Treatment of categorical mediator LATENT
Algorithm used for Markov chain Monte Carlo GIBBS(PX1)
Convergence criterion 0.500D-01
Maximum number of iterations 50000
K-th iteration used for thinning 1
Link PROBIT
Input data file(s)
ex9.21.dat
Input data format FREE
SUMMARY OF DATA
Number of LEVEL2 clusters 1500
Number of LEVEL3 clusters 50
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
U
Category 1 0.495 3715.000
Category 2 0.505 3785.000
UNIVARIATE SAMPLE STATISTICS
UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS
Variable/ Mean/ Skewness/ Minimum/ % with Percentiles
Sample Size Variance Kurtosis Maximum Min/Max 20%/60% 40%/80% Median
Y2 0.070 -0.053 -4.350 0.07% -1.102 -0.286 0.083
1500.000 1.992 -0.136 5.051 0.07% 0.439 1.309
Y 0.080 -0.046 -6.022 0.01% -1.286 -0.301 0.098
7500.000 2.617 0.012 6.238 0.01% 0.483 1.443
Y3 -0.079 -0.190 -2.194 2.00% -0.851 -0.315 -0.024
50.000 0.786 -0.192 1.734 2.00% 0.225 0.509
X 0.008 0.008 -4.119 0.01% -0.842 -0.260 0.001
7500.000 1.013 0.013 4.022 0.01% 0.268 0.856
W 0.030 -0.083 -3.508 0.07% -0.792 -0.208 0.029
1500.000 1.007 0.037 2.958 0.07% 0.269 0.851
Z 0.017 -0.103 -2.337 2.00% -0.642 -0.245 -0.036
50.000 0.823 -0.067 2.055 2.00% 0.254 0.731
THE MODEL ESTIMATION TERMINATED NORMALLY
USE THE FBITERATIONS OPTION TO INCREASE THE NUMBER OF ITERATIONS BY A FACTOR
OF AT LEAST TWO TO CHECK CONVERGENCE AND THAT THE PSR VALUE DOES NOT INCREASE.
MODEL FIT INFORMATION
Number of Free Parameters 29
Bayesian Posterior Predictive Checking using Chi-Square
95% Confidence Interval for the Difference Between
the Observed and the Replicated Chi-Square Values
-28.948 25.213
Posterior Predictive P-Value 0.618
MODEL RESULTS
Posterior One-Tailed 95% C.I.
Estimate S.D. P-Value Lower 2.5% Upper 2.5% Significance
Within Level
U ON
Y 0.753 0.030 0.000 0.693 0.807 *
X 0.483 0.029 0.000 0.430 0.544 *
Y ON
X 0.249 0.012 0.000 0.225 0.273 *
Residual Variances
Y 1.010 0.019 0.000 0.974 1.048 *
Between LEVEL2 Level
U ON
W 1.079 0.052 0.000 0.987 1.183 *
Y 0.516 0.065 0.000 0.383 0.642 *
Y2 0.596 0.059 0.000 0.475 0.700 *
Y ON
W 0.490 0.022 0.000 0.442 0.532 *
Y2 ON
W 0.682 0.018 0.000 0.644 0.718 *
Y WITH
Y2 0.255 0.018 0.000 0.222 0.290 *
Residual Variances
U 0.371 0.041 0.000 0.283 0.448 *
Y2 0.478 0.017 0.000 0.446 0.513 *
Y 0.496 0.026 0.000 0.448 0.547 *
Between LEVEL3 Level
U ON
Y 0.597 0.215 0.004 0.176 1.044 *
Y2 0.849 0.186 0.000 0.479 1.213 *
Y ON
Z 0.637 0.119 0.000 0.407 0.873 *
Y2 ON
Z 0.776 0.130 0.000 0.521 1.032 *
Y3 ON
Y 0.313 0.215 0.065 -0.116 0.731
Y2 0.290 0.185 0.065 -0.079 0.644
Y WITH
Y2 0.361 0.101 0.000 0.203 0.601 *
U WITH
Y3 0.229 0.092 0.000 0.091 0.452 *
Intercepts
Y2 0.032 0.114 0.380 -0.194 0.248
Y 0.045 0.109 0.342 -0.167 0.249
Y3 -0.120 0.103 0.122 -0.323 0.081
Thresholds
U$1 0.120 0.107 0.129 -0.086 0.331
Residual Variances
U 0.513 0.124 0.000 0.324 0.822 *
Y2 0.593 0.127 0.000 0.410 0.887 *
Y 0.510 0.115 0.000 0.352 0.807 *
Y3 0.526 0.120 0.000 0.354 0.841 *
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
TAU
U$1
________
0
NU
U Y X
________ ________ ________
0 0 0
LAMBDA
U Y X
________ ________ ________
U 0 0 0
Y 0 0 0
X 0 0 0
THETA
U Y X
________ ________ ________
U 0
Y 0 0
X 0 0 0
ALPHA
U Y X
________ ________ ________
0 0 0
BETA
U Y X
________ ________ ________
U 0 1 2
Y 0 0 3
X 0 0 0
PSI
U Y X
________ ________ ________
U 0
Y 0 4
X 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN LEVEL2
TAU
U$1
________
0
NU
U Y2 Y W
________ ________ ________ ________
0 0 0 0
LAMBDA
U Y2 Y W
________ ________ ________ ________
U 0 0 0 0
Y2 0 0 0 0
Y 0 0 0 0
W 0 0 0 0
THETA
U Y2 Y W
________ ________ ________ ________
U 0
Y2 0 0
Y 0 0 0
W 0 0 0 0
ALPHA
U Y2 Y W
________ ________ ________ ________
0 0 0 0
BETA
U Y2 Y W
________ ________ ________ ________
U 0 5 6 7
Y2 0 0 0 8
Y 0 0 0 9
W 0 0 0 0
PSI
U Y2 Y W
________ ________ ________ ________
U 10
Y2 0 11
Y 0 12 13
W 0 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN LEVEL3
TAU
U$1
________
29
NU
U Y2 Y Y3 Z
________ ________ ________ ________ ________
0 0 0 0 0
LAMBDA
U Y2 Y Y3 Z
________ ________ ________ ________ ________
U 0 0 0 0 0
Y2 0 0 0 0 0
Y 0 0 0 0 0
Y3 0 0 0 0 0
Z 0 0 0 0 0
THETA
U Y2 Y Y3 Z
________ ________ ________ ________ ________
U 0
Y2 0 0
Y 0 0 0
Y3 0 0 0 0
Z 0 0 0 0 0
ALPHA
U Y2 Y Y3 Z
________ ________ ________ ________ ________
0 14 15 16 0
BETA
U Y2 Y Y3 Z
________ ________ ________ ________ ________
U 0 17 18 0 0
Y2 0 0 0 0 19
Y 0 0 0 0 20
Y3 0 21 22 0 0
Z 0 0 0 0 0
PSI
U Y2 Y Y3 Z
________ ________ ________ ________ ________
U 23
Y2 0 24
Y 0 25 26
Y3 27 0 0 28
Z 0 0 0 0 0
STARTING VALUES FOR WITHIN
TAU
U$1
________
0.000
NU
U Y X
________ ________ ________
0.000 0.000 0.000
LAMBDA
U Y X
________ ________ ________
U 1.000 0.000 0.000
Y 0.000 1.000 0.000
X 0.000 0.000 1.000
THETA
U Y X
________ ________ ________
U 0.000
Y 0.000 0.000
X 0.000 0.000 0.000
ALPHA
U Y X
________ ________ ________
0.000 0.000 0.000
BETA
U Y X
________ ________ ________
U 0.000 0.000 0.000
Y 0.000 0.000 0.000
X 0.000 0.000 0.000
PSI
U Y X
________ ________ ________
U 1.000
Y 0.000 1.308
X 0.000 0.000 0.507
STARTING VALUES FOR BETWEEN LEVEL2
TAU
U$1
________
0.000
NU
U Y2 Y W
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
U Y2 Y W
________ ________ ________ ________
U 1.000 0.000 0.000 0.000
Y2 0.000 1.000 0.000 0.000
Y 0.000 0.000 1.000 0.000
W 0.000 0.000 0.000 1.000
THETA
U Y2 Y W
________ ________ ________ ________
U 0.000
Y2 0.000 0.000
Y 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000
ALPHA
U Y2 Y W
________ ________ ________ ________
0.000 0.000 0.000 0.000
BETA
U Y2 Y W
________ ________ ________ ________
U 0.000 0.000 0.000 0.000
Y2 0.000 0.000 0.000 0.000
Y 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000
PSI
U Y2 Y W
________ ________ ________ ________
U 1.000
Y2 0.000 0.996
Y 0.000 0.000 1.308
W 0.000 0.000 0.000 0.504
STARTING VALUES FOR BETWEEN LEVEL3
TAU
U$1
________
-0.010
NU
U Y2 Y Y3 Z
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
U Y2 Y Y3 Z
________ ________ ________ ________ ________
U 1.000 0.000 0.000 0.000 0.000
Y2 0.000 1.000 0.000 0.000 0.000
Y 0.000 0.000 1.000 0.000 0.000
Y3 0.000 0.000 0.000 1.000 0.000
Z 0.000 0.000 0.000 0.000 1.000
THETA
U Y2 Y Y3 Z
________ ________ ________ ________ ________
U 0.000
Y2 0.000 0.000
Y 0.000 0.000 0.000
Y3 0.000 0.000 0.000 0.000
Z 0.000 0.000 0.000 0.000 0.000
ALPHA
U Y2 Y Y3 Z
________ ________ ________ ________ ________
0.000 0.070 0.080 -0.079 0.000
BETA
U Y2 Y Y3 Z
________ ________ ________ ________ ________
U 0.000 0.000 0.000 0.000 0.000
Y2 0.000 0.000 0.000 0.000 0.000
Y 0.000 0.000 0.000 0.000 0.000
Y3 0.000 0.000 0.000 0.000 0.000
Z 0.000 0.000 0.000 0.000 0.000
PSI
U Y2 Y Y3 Z
________ ________ ________ ________ ________
U 1.000
Y2 0.000 0.996
Y 0.000 0.000 1.308
Y3 0.000 0.000 0.000 0.393
Z 0.000 0.000 0.000 0.000 0.412
PRIORS FOR ALL PARAMETERS PRIOR MEAN PRIOR VARIANCE PRIOR STD. DEV.
Parameter 1~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 2~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 3~N(0.000,infinity) 0.0000 infinity infinity
Parameter 4~IG(-1.000,0.000) infinity infinity infinity
Parameter 5~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 6~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 7~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 8~N(0.000,infinity) 0.0000 infinity infinity
Parameter 9~N(0.000,infinity) 0.0000 infinity infinity
Parameter 10~IG(-1.000,0.000) infinity infinity infinity
Parameter 11~IW(1.000,3) infinity infinity infinity
Parameter 12~IW(0.000,3) infinity infinity infinity
Parameter 13~IW(1.000,3) infinity infinity infinity
Parameter 14~N(0.000,infinity) 0.0000 infinity infinity
Parameter 15~N(0.000,infinity) 0.0000 infinity infinity
Parameter 16~N(0.000,infinity) 0.0000 infinity infinity
Parameter 17~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 18~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 19~N(0.000,infinity) 0.0000 infinity infinity
Parameter 20~N(0.000,infinity) 0.0000 infinity infinity
Parameter 21~N(0.000,infinity) 0.0000 infinity infinity
Parameter 22~N(0.000,infinity) 0.0000 infinity infinity
Parameter 23~IW(1.000,3) infinity infinity infinity
Parameter 24~IW(1.000,3) infinity infinity infinity
Parameter 25~IW(0.000,3) infinity infinity infinity
Parameter 26~IW(1.000,3) infinity infinity infinity
Parameter 27~IW(0.000,3) infinity infinity infinity
Parameter 28~IW(1.000,3) infinity infinity infinity
Parameter 29~N(0.000,5.000) 0.0000 5.0000 2.2361
TECHNICAL 8 OUTPUT
Kolmogorov-Smirnov comparing posterior distributions across chains 1 and 2 using 100 draws.
Parameter KS Statistic P-value
Parameter 20 0.1500 0.1930
Parameter 21 0.1500 0.1930
Parameter 17 0.1400 0.2606
Parameter 10 0.1300 0.3439
Parameter 22 0.1200 0.4431
Parameter 5 0.1100 0.5560
Parameter 19 0.1100 0.5560
Parameter 18 0.1000 0.6766
Parameter 2 0.1000 0.6766
Parameter 7 0.1000 0.6766
Parameter 29 0.1000 0.6766
Parameter 15 0.1000 0.6766
Parameter 25 0.0900 0.7942
Parameter 24 0.0800 0.8938
Parameter 27 0.0700 0.9610
Parameter 26 0.0700 0.9610
Parameter 28 0.0600 0.9921
Parameter 16 0.0500 0.9995
Parameter 23 0.0500 0.9995
Parameter 14 0.0400 1.0000
Parameter 6 0.0400 1.0000
Parameter 12 0.0300 1.0000
Parameter 11 0.0200 1.0000
Parameter 13 0.0200 1.0000
Parameter 9 0.0200 1.0000
Parameter 1 0.0100 1.0000
Parameter 8 0.0000 1.0000
Parameter 4 0.0000 1.0000
Parameter 3 0.0000 1.0000
Simulated prior distributions
Parameter Prior Mean Prior Variance Prior Std. Dev.
Parameter 1 -0.1382 4.9205 2.2182
Parameter 2 -0.0169 4.6231 2.1501
Parameter 3 Improper Prior
Parameter 4 Improper Prior
Parameter 5 -0.0110 5.0352 2.2439
Parameter 6 -0.0174 4.7349 2.1760
Parameter 7 0.0125 4.5938 2.1433
Parameter 8 Improper Prior
Parameter 9 Improper Prior
Parameter 10 Improper Prior
Parameter 11 3.4960 612.3356 24.7454
Parameter 12 -1.2021 1020.6331 31.9473
Parameter 13 4.5093 2355.3237 48.5317
Parameter 14 Improper Prior
Parameter 15 Improper Prior
Parameter 16 Improper Prior
Parameter 17 -0.0666 4.9574 2.2265
Parameter 18 -0.0980 4.5063 2.1228
Parameter 19 Improper Prior
Parameter 20 Improper Prior
Parameter 21 Improper Prior
Parameter 22 Improper Prior
Parameter 23 6.1610 5329.3192 73.0022
Parameter 24 4.2149 760.9879 27.5860
Parameter 25 -1.5619 2384.6592 48.8330
Parameter 26 38.4703 1214949.8527 1102.2476
Parameter 27 -0.3215 996.6667 31.5700
Parameter 28 3.8240 389.4822 19.7353
Parameter 29 0.0940 5.1061 2.2597
TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION
CHAIN BSEED
1 0
2 285380
POTENTIAL PARAMETER WITH
ITERATION SCALE REDUCTION HIGHEST PSR
100 1.397 10
200 1.082 7
300 1.278 10
400 1.096 7
500 1.027 2
600 1.118 7
700 1.103 7
800 1.144 7
900 1.088 7
1000 1.030 2
Beginning Time: 04:53:58
Ending Time: 04:54:10
Elapsed Time: 00:00:12
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