Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:20 PM
INPUT INSTRUCTIONS
TITLE: this is an example of regression with cross-
classified data
DATA: FILE = ex9.24.dat;
VARIABLE: NAMES = y x1 x2 w z level2a level2b;
CLUSTER = level2b level2a;
WITHIN = x1 x2;
BETWEEN = (level2a) w (level2b) z;
ANALYSIS: TYPE = CROSSCLASSIFIED RANDOM;
ESTIMATOR = BAYES;
PROCESSORS = 2;
BITER = (2000);
MODEL: %WITHIN%
y ON x1;
s | y ON x2;
%BETWEEN level2a%
y ON w;
s ON w;
y WITH s;
%BETWEEN level2b%
y ON z;
s ON Z;
y WITH s;
OUTPUT: TECH1 TECH8;
INPUT READING TERMINATED NORMALLY
this is an example of regression with cross-
classified data
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 3000
Number of dependent variables 1
Number of independent variables 4
Number of continuous latent variables 1
Observed dependent variables
Continuous
Y
Observed independent variables
X1 X2 W Z
Continuous latent variables
S
Variables with special functions
Cluster variables LEVEL2B LEVEL2A
Within variables
X1 X2
Level 2a between variables
W
Level 2b between variables
Z
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
Input data file(s)
ex9.24.dat
Input data format FREE
SUMMARY OF DATA
Cluster information for LEVEL2A
Number of clusters 30
Size (s) Cluster ID with Size s
100 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
22 23 24 25 26 27 28 29 30
Cluster information for LEVEL2B
Number of clusters 50
Size (s) Cluster ID with Size s
60 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49 50
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
Y 1.938 0.148 -7.667 0.03% -0.294 1.269 1.831
3000.000 7.602 0.422 13.976 0.03% 2.479 4.142
X1 -0.021 -0.047 -3.801 0.03% -0.853 -0.271 -0.020
3000.000 0.983 0.070 3.610 0.03% 0.219 0.811
X2 0.018 -0.016 -3.558 0.03% -0.808 -0.243 0.019
3000.000 1.028 0.067 4.267 0.03% 0.274 0.858
W 0.135 0.109 -1.729 3.33% -0.965 -0.092 0.284
30.000 1.167 -0.281 2.816 3.33% 0.518 0.954
Z 0.160 0.016 -2.058 2.00% -0.691 -0.152 0.300
50.000 1.030 -0.040 2.716 2.00% 0.433 0.977
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 14
Information Criteria
Deviance (DIC) 10690.173
Estimated Number of Parameters (pD) 148.893
MODEL RESULTS
Posterior One-Tailed 95% C.I.
Estimate S.D. P-Value Lower 2.5% Upper 2.5% Significance
Within Level
Y ON
X1 0.998 0.026 0.000 0.947 1.047 *
Residual Variances
Y 1.968 0.053 0.000 1.867 2.075 *
Between LEVEL2A Level
S ON
W 0.512 0.139 0.000 0.233 0.784 *
Y ON
W 0.630 0.214 0.002 0.202 1.049 *
Y WITH
S 0.014 0.225 0.468 -0.471 0.456
Residual Variances
Y 1.511 0.524 0.000 0.891 2.828 *
S 0.599 0.215 0.000 0.348 1.157 *
Between LEVEL2B Level
S ON
Z 0.335 0.064 0.000 0.209 0.468 *
Y ON
Z 0.674 0.121 0.000 0.424 0.901 *
Y WITH
S 0.008 0.061 0.449 -0.113 0.130
Intercepts
Y 1.569 0.292 0.000 0.970 2.074 *
S 0.908 0.161 0.000 0.546 1.195 *
Residual Variances
Y 0.686 0.163 0.000 0.452 1.092 *
S 0.162 0.046 0.000 0.100 0.280 *
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
NU
Y X1 X2
________ ________ ________
0 0 0
LAMBDA
Y X1 X2
________ ________ ________
Y 0 0 0
X1 0 0 0
X2 0 0 0
THETA
Y X1 X2
________ ________ ________
Y 0
X1 0 0
X2 0 0 0
ALPHA
Y X1 X2
________ ________ ________
0 0 0
BETA
Y X1 X2
________ ________ ________
Y 0 1 0
X1 0 0 0
X2 0 0 0
PSI
Y X1 X2
________ ________ ________
Y 2
X1 0 0
X2 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN LEVEL2A
NU
Y W
________ ________
0 0
LAMBDA
S%2a Y W
________ ________ ________
Y 0 0 0
W 0 0 0
THETA
Y W
________ ________
Y 0
W 0 0
ALPHA
S%2a Y W
________ ________ ________
0 0 0
BETA
S%2a Y W
________ ________ ________
S%2a 0 0 3
Y 0 0 4
W 0 0 0
PSI
S%2a Y W
________ ________ ________
S%2a 5
Y 6 7
W 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN LEVEL2B
NU
Y Z
________ ________
0 0
LAMBDA
S%2b Y Z
________ ________ ________
Y 0 0 0
Z 0 0 0
THETA
Y Z
________ ________
Y 0
Z 0 0
ALPHA
S%2b Y Z
________ ________ ________
8 9 0
BETA
S%2b Y Z
________ ________ ________
S%2b 0 0 10
Y 0 0 11
Z 0 0 0
PSI
S%2b Y Z
________ ________ ________
S%2b 12
Y 13 14
Z 0 0 0
STARTING VALUES FOR WITHIN
NU
Y X1 X2
________ ________ ________
0.000 0.000 0.000
LAMBDA
Y X1 X2
________ ________ ________
Y 1.000 0.000 0.000
X1 0.000 1.000 0.000
X2 0.000 0.000 1.000
THETA
Y X1 X2
________ ________ ________
Y 0.000
X1 0.000 0.000
X2 0.000 0.000 0.000
ALPHA
Y X1 X2
________ ________ ________
0.000 0.000 0.000
BETA
Y X1 X2
________ ________ ________
Y 0.000 0.000 0.000
X1 0.000 0.000 0.000
X2 0.000 0.000 0.000
PSI
Y X1 X2
________ ________ ________
Y 3.801
X1 0.000 0.492
X2 0.000 0.000 0.514
STARTING VALUES FOR BETWEEN LEVEL2A
NU
Y W
________ ________
0.000 0.000
LAMBDA
S%2a Y W
________ ________ ________
Y 0.000 1.000 0.000
W 0.000 0.000 1.000
THETA
Y W
________ ________
Y 0.000
W 0.000 0.000
ALPHA
S%2a Y W
________ ________ ________
0.000 0.000 0.000
BETA
S%2a Y W
________ ________ ________
S%2a 0.000 0.000 0.000
Y 0.000 0.000 0.000
W 0.000 0.000 0.000
PSI
S%2a Y W
________ ________ ________
S%2a 1.000
Y 0.000 3.801
W 0.000 0.000 0.584
STARTING VALUES FOR BETWEEN LEVEL2B
NU
Y Z
________ ________
0.000 0.000
LAMBDA
S%2b Y Z
________ ________ ________
Y 0.000 1.000 0.000
Z 0.000 0.000 1.000
THETA
Y Z
________ ________
Y 0.000
Z 0.000 0.000
ALPHA
S%2b Y Z
________ ________ ________
0.000 1.938 0.000
BETA
S%2b Y Z
________ ________ ________
S%2b 0.000 0.000 0.000
Y 0.000 0.000 0.000
Z 0.000 0.000 0.000
PSI
S%2b Y Z
________ ________ ________
S%2b 1.000
Y 0.000 3.801
Z 0.000 0.000 0.515
PRIORS FOR ALL PARAMETERS PRIOR MEAN PRIOR VARIANCE PRIOR STD. DEV.
Parameter 1~N(0.000,infinity) 0.0000 infinity infinity
Parameter 2~IG(-1.000,0.000) infinity infinity infinity
Parameter 3~N(0.000,infinity) 0.0000 infinity infinity
Parameter 4~N(0.000,infinity) 0.0000 infinity infinity
Parameter 5~IW(0.000,-3) infinity infinity infinity
Parameter 6~IW(0.000,-3) infinity infinity infinity
Parameter 7~IW(0.000,-3) infinity infinity infinity
Parameter 8~N(0.000,infinity) 0.0000 infinity infinity
Parameter 9~N(0.000,infinity) 0.0000 infinity infinity
Parameter 10~N(0.000,infinity) 0.0000 infinity infinity
Parameter 11~N(0.000,infinity) 0.0000 infinity infinity
Parameter 12~IW(0.000,-3) infinity infinity infinity
Parameter 13~IW(0.000,-3) infinity infinity infinity
Parameter 14~IW(0.000,-3) infinity infinity infinity
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION
CHAIN BSEED
1 0
2 285380
POTENTIAL PARAMETER WITH
ITERATION SCALE REDUCTION HIGHEST PSR
100 1.135 8
200 1.259 9
300 2.020 9
400 2.133 9
500 1.433 8
600 1.372 8
700 1.276 9
800 1.367 9
900 1.549 9
1000 1.384 9
1100 1.282 9
1200 1.076 9
1300 1.018 9
1400 1.053 9
1500 1.090 9
1600 1.064 9
1700 1.016 9
1800 1.007 7
1900 1.008 7
2000 1.007 7
Beginning Time: 23:20:58
Ending Time: 23:21:01
Elapsed Time: 00:00:03
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