Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:20 PM
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
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
-27.924 29.008
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
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: 23:20:46
Ending Time: 23:20:53
Elapsed Time: 00:00:07
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