Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:21 PM
INPUT INSTRUCTIONS
TITLE: this is an example of path analysis with cross-
classified data
DATA: FILE = ex9.25.dat;
VARIABLE: NAMES = y1 y2 x w z level2a level2b;
CLUSTER = level2b level2a;
WITHIN = x;
BETWEEN = (level2a) w (level2b) z;
ANALYSIS: TYPE = CROSSCLASSIFIED;
ESTIMATOR = BAYES;
PROCESSORS = 2;
MODEL: %WITHIN%
y2 ON y1 x;
y1 ON x;
%BETWEEN level2a%
y1-y2 ON w;
y1 WITH y2;
%BETWEEN level2b%
y1-y2 ON z;
y1 WITH y2;
OUTPUT: TECH1 TECH8;
INPUT READING TERMINATED NORMALLY
this is an example of path analysis with cross-
classified data
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 2000
Number of dependent variables 2
Number of independent variables 3
Number of continuous latent variables 0
Observed dependent variables
Continuous
Y1 Y2
Observed independent variables
X W Z
Variables with special functions
Cluster variables LEVEL2B LEVEL2A
Within variables
X
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)
ex9.25.dat
Input data format FREE
SUMMARY OF DATA
Cluster information for LEVEL2A
Number of clusters 20
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
Cluster information for LEVEL2B
Number of clusters 100
Size (s) Cluster ID with Size s
20 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 51 52 53 54 55 56 57
58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93
94 95 96 97 98 99 100
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
Y1 1.421 -0.102 -5.026 0.05% -0.132 0.989 1.444
2000.000 3.494 -0.061 6.864 0.05% 1.908 3.030
Y2 1.623 0.045 -4.604 0.05% -0.001 1.149 1.631
2000.000 3.485 -0.176 8.026 0.05% 2.118 3.216
X -0.032 0.061 -2.910 0.05% -0.879 -0.304 -0.040
2000.000 1.012 -0.180 3.275 0.05% 0.208 0.833
W -0.131 -0.047 -1.980 5.00% -1.612 -0.890 0.186
20.000 1.436 -1.448 1.614 5.00% 0.421 0.885
Z 0.013 0.090 -2.058 1.00% -0.828 -0.231 -0.018
100.000 0.951 -0.170 2.351 1.00% 0.263 0.777
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 17
Bayesian Posterior Predictive Checking using Chi-Square
95% Confidence Interval for the Difference Between
the Observed and the Replicated Chi-Square Values
-13.833 22.183
Posterior Predictive P-Value 0.439
Information Criteria
Deviance (DIC) 11772.253
Estimated Number of Parameters (pD) 223.817
MODEL RESULTS
Posterior One-Tailed 95% C.I.
Estimate S.D. P-Value Lower 2.5% Upper 2.5% Significance
Within Level
Y2 ON
Y1 0.509 0.023 0.000 0.467 0.554 *
X -0.016 0.029 0.305 -0.074 0.038
Y1 ON
X 0.722 0.024 0.000 0.675 0.770 *
Residual Variances
Y1 1.038 0.034 0.000 0.973 1.105 *
Y2 1.063 0.035 0.000 1.000 1.137 *
Between LEVEL2A Level
Y1 ON
W 0.635 0.181 0.001 0.281 0.991 *
Y2 ON
W 0.469 0.192 0.010 0.087 0.874 *
Y1 WITH
Y2 0.091 0.301 0.331 -0.414 0.765
Residual Variances
Y1 0.933 0.427 0.000 0.449 2.067 *
Y2 1.048 0.460 0.000 0.513 2.328 *
Between LEVEL2B Level
Y1 ON
Z 0.334 0.080 0.000 0.165 0.488 *
Y2 ON
Z 0.651 0.087 0.000 0.465 0.813 *
Y1 WITH
Y2 0.006 0.070 0.460 -0.132 0.140
Intercepts
Y1 1.379 0.175 0.000 0.965 1.675 *
Y2 1.496 0.211 0.000 1.154 2.019 *
Residual Variances
Y1 0.533 0.090 0.000 0.389 0.747 *
Y2 0.662 0.112 0.000 0.488 0.915 *
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
NU
Y1 Y2 X
________ ________ ________
0 0 0
LAMBDA
Y1 Y2 X
________ ________ ________
Y1 0 0 0
Y2 0 0 0
X 0 0 0
THETA
Y1 Y2 X
________ ________ ________
Y1 0
Y2 0 0
X 0 0 0
ALPHA
Y1 Y2 X
________ ________ ________
0 0 0
BETA
Y1 Y2 X
________ ________ ________
Y1 0 0 1
Y2 2 0 3
X 0 0 0
PSI
Y1 Y2 X
________ ________ ________
Y1 4
Y2 0 5
X 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN LEVEL2A
NU
Y1 Y2 W
________ ________ ________
0 0 0
LAMBDA
Y1 Y2 W
________ ________ ________
Y1 0 0 0
Y2 0 0 0
W 0 0 0
THETA
Y1 Y2 W
________ ________ ________
Y1 0
Y2 0 0
W 0 0 0
ALPHA
Y1 Y2 W
________ ________ ________
0 0 0
BETA
Y1 Y2 W
________ ________ ________
Y1 0 0 6
Y2 0 0 7
W 0 0 0
PSI
Y1 Y2 W
________ ________ ________
Y1 8
Y2 9 10
W 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN LEVEL2B
NU
Y1 Y2 Z
________ ________ ________
0 0 0
LAMBDA
Y1 Y2 Z
________ ________ ________
Y1 0 0 0
Y2 0 0 0
Z 0 0 0
THETA
Y1 Y2 Z
________ ________ ________
Y1 0
Y2 0 0
Z 0 0 0
ALPHA
Y1 Y2 Z
________ ________ ________
11 12 0
BETA
Y1 Y2 Z
________ ________ ________
Y1 0 0 13
Y2 0 0 14
Z 0 0 0
PSI
Y1 Y2 Z
________ ________ ________
Y1 15
Y2 16 17
Z 0 0 0
STARTING VALUES FOR WITHIN
NU
Y1 Y2 X
________ ________ ________
0.000 0.000 0.000
LAMBDA
Y1 Y2 X
________ ________ ________
Y1 1.000 0.000 0.000
Y2 0.000 1.000 0.000
X 0.000 0.000 1.000
THETA
Y1 Y2 X
________ ________ ________
Y1 0.000
Y2 0.000 0.000
X 0.000 0.000 0.000
ALPHA
Y1 Y2 X
________ ________ ________
0.000 0.000 0.000
BETA
Y1 Y2 X
________ ________ ________
Y1 0.000 0.000 0.000
Y2 0.000 0.000 0.000
X 0.000 0.000 0.000
PSI
Y1 Y2 X
________ ________ ________
Y1 1.747
Y2 0.000 1.743
X 0.000 0.000 0.506
STARTING VALUES FOR BETWEEN LEVEL2A
NU
Y1 Y2 W
________ ________ ________
0.000 0.000 0.000
LAMBDA
Y1 Y2 W
________ ________ ________
Y1 1.000 0.000 0.000
Y2 0.000 1.000 0.000
W 0.000 0.000 1.000
THETA
Y1 Y2 W
________ ________ ________
Y1 0.000
Y2 0.000 0.000
W 0.000 0.000 0.000
ALPHA
Y1 Y2 W
________ ________ ________
0.000 0.000 0.000
BETA
Y1 Y2 W
________ ________ ________
Y1 0.000 0.000 0.000
Y2 0.000 0.000 0.000
W 0.000 0.000 0.000
PSI
Y1 Y2 W
________ ________ ________
Y1 1.747
Y2 0.000 1.743
W 0.000 0.000 0.718
STARTING VALUES FOR BETWEEN LEVEL2B
NU
Y1 Y2 Z
________ ________ ________
0.000 0.000 0.000
LAMBDA
Y1 Y2 Z
________ ________ ________
Y1 1.000 0.000 0.000
Y2 0.000 1.000 0.000
Z 0.000 0.000 1.000
THETA
Y1 Y2 Z
________ ________ ________
Y1 0.000
Y2 0.000 0.000
Z 0.000 0.000 0.000
ALPHA
Y1 Y2 Z
________ ________ ________
1.421 1.623 0.000
BETA
Y1 Y2 Z
________ ________ ________
Y1 0.000 0.000 0.000
Y2 0.000 0.000 0.000
Z 0.000 0.000 0.000
PSI
Y1 Y2 Z
________ ________ ________
Y1 1.747
Y2 0.000 1.743
Z 0.000 0.000 0.475
PRIORS FOR ALL PARAMETERS PRIOR MEAN PRIOR VARIANCE PRIOR STD. DEV.
Parameter 1~N(0.000,infinity) 0.0000 infinity infinity
Parameter 2~N(0.000,infinity) 0.0000 infinity infinity
Parameter 3~N(0.000,infinity) 0.0000 infinity infinity
Parameter 4~IG(-1.000,0.000) infinity infinity infinity
Parameter 5~IG(-1.000,0.000) infinity infinity infinity
Parameter 6~N(0.000,infinity) 0.0000 infinity infinity
Parameter 7~N(0.000,infinity) 0.0000 infinity infinity
Parameter 8~IW(0.000,-3) infinity infinity infinity
Parameter 9~IW(0.000,-3) infinity infinity infinity
Parameter 10~IW(0.000,-3) infinity infinity infinity
Parameter 11~N(0.000,infinity) 0.0000 infinity infinity
Parameter 12~N(0.000,infinity) 0.0000 infinity infinity
Parameter 13~N(0.000,infinity) 0.0000 infinity infinity
Parameter 14~N(0.000,infinity) 0.0000 infinity infinity
Parameter 15~IW(0.000,-3) infinity infinity infinity
Parameter 16~IW(0.000,-3) infinity infinity infinity
Parameter 17~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 2.080 11
200 1.145 12
300 1.189 12
400 1.598 12
500 2.121 12
600 1.744 12
700 1.232 12
800 1.023 12
Beginning Time: 23:21:01
Ending Time: 23:21:02
Elapsed Time: 00:00:01
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