Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:27 PM
INPUT INSTRUCTIONS
TITLE: this is an example of path analysis with cross-
classified data
montecarlo:
names = y1 y2 x w z;
within = x;
between = (level2a) w (level2b) z;
nobs = 2000;
nreps =1;
! 100 level2b units and 20 level2a units:
csizes = 100[20(1)];
ncsizes = 1[1];
save = ex9.25.dat;
analysis:
type = crossclassified random;
estimator = bayes;
processors = 2;
biter = (2000);
model population:
%within%
x@1;
y2 on y1*.5
x*0;
y1 on x*.7;
y1-y2*1;
%between level2a%
w@1;
y1 on w*.6;
y2 on w*.3;
y1-y2*.5;
y1 with y2*0;
%between level2b%
z@1;
y1 on z*.3;
y2 on z*.6;
y1-y2*.5;
y1 with y2*0;
[y1-y2*1.5];
model:
%within%
! x@1;
y2 on y1*.5
x*0;
y1 on x*.7;
y1-y2*1;
%between level2a%
! w@1;
y1 on w*.6;
y2 on w*.3;
y1-y2*.5;
y1 with y2*0;
%between level2b%
! z@1;
y1 on z*.3;
y2 on z*.6;
y1-y2*.5;
y1 with y2*0;
[y1-y2*1.5];
output: 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 replications
Requested 1
Completed 1
Value of seed 0
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
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
SUMMARY OF DATA FOR THE FIRST REPLICATION
Cluster information
Number of level 2a clusters 20
Number of level 2b clusters 100
MODEL FIT INFORMATION
Number of Free Parameters 17
Bayesian Posterior Predictive Checking using Chi-Square
Posterior Predictive P-Value
Mean 0.378
Std Dev 0.000
Number of successful computations 1
Cumulative Distribution Function
Value Function Value
0.990 1.000
0.980 1.000
0.950 1.000
0.900 1.000
0.800 1.000
0.700 1.000
0.500 1.000
0.300 0.000
0.200 0.000
0.100 0.000
0.050 0.000
0.020 0.000
0.010 0.000
Information Criteria
Deviance (DIC)
Mean 11770.548
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 11770.548 11770.548
0.980 0.000 11770.548 11770.548
0.950 0.000 11770.548 11770.548
0.900 0.000 11770.548 11770.548
0.800 0.000 11770.548 11770.548
0.700 0.000 11770.548 11770.548
0.500 0.000 11770.548 11770.548
0.300 0.000 11770.548 11770.548
0.200 0.000 11770.548 11770.548
0.100 0.000 11770.548 11770.548
0.050 0.000 11770.548 11770.548
0.020 0.000 11770.548 11770.548
0.010 0.000 11770.548 11770.548
Estimated Number of Parameters (pD)
Mean 223.776
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 223.776 223.776
0.980 0.000 223.776 223.776
0.950 0.000 223.776 223.776
0.900 0.000 223.776 223.776
0.800 0.000 223.776 223.776
0.700 0.000 223.776 223.776
0.500 0.000 223.776 223.776
0.300 0.000 223.776 223.776
0.200 0.000 223.776 223.776
0.100 0.000 223.776 223.776
0.050 0.000 223.776 223.776
0.020 0.000 223.776 223.776
0.010 0.000 223.776 223.776
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Within Level
Y2 ON
Y1 0.500 0.5074 0.0000 0.0235 0.0001 1.000 1.000
X 0.000 -0.0143 0.0000 0.0284 0.0002 1.000 0.000
Y1 ON
X 0.700 0.7226 0.0000 0.0237 0.0005 1.000 1.000
Residual Variances
Y1 1.000 1.0372 0.0000 0.0332 0.0014 1.000 1.000
Y2 1.000 1.0650 0.0000 0.0349 0.0042 1.000 1.000
Between LEVEL2A Level
Y1 ON
W 0.600 0.6489 0.0000 0.2019 0.0024 1.000 1.000
Y2 ON
W 0.300 0.4953 0.0000 0.2025 0.0381 1.000 1.000
Y1 WITH
Y2 0.000 0.0435 0.0000 0.3682 0.0019 1.000 0.000
Residual Variances
Y1 0.500 0.9937 0.0000 0.5170 0.2437 1.000 1.000
Y2 0.500 1.0627 0.0000 0.5109 0.3167 0.000 1.000
Between LEVEL2B Level
Y1 ON
Z 0.300 0.3352 0.0000 0.0802 0.0012 1.000 1.000
Y2 ON
Z 0.600 0.6501 0.0000 0.0873 0.0025 1.000 1.000
Y1 WITH
Y2 0.000 0.0098 0.0000 0.0697 0.0001 1.000 0.000
Intercepts
Y1 1.500 1.5615 0.0000 0.3197 0.0038 1.000 1.000
Y2 1.500 1.7641 0.0000 0.2619 0.0697 1.000 1.000
Residual Variances
Y1 0.500 0.5358 0.0000 0.0884 0.0013 1.000 1.000
Y2 0.500 0.6519 0.0000 0.1093 0.0231 1.000 1.000
CORRELATIONS AND MEAN SQUARE ERROR OF THE TRUE FACTOR VALUES AND THE FACTOR SCORES
CORRELATIONS MEAN SQUARE ERROR
Average Std. Dev. Average Std. Dev.
B2a_Y1 0.993 0.000 0.136 0.000
B2a_Y2 0.994 0.000 0.169 0.000
B2b_Y1 0.968 0.000 0.202 0.000
B2b_Y2 0.965 0.000 0.289 0.000
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 0.700
Y2 0.500 0.000 0.000
X 0.000 0.000 0.000
PSI
Y1 Y2 X
________ ________ ________
Y1 1.000
Y2 0.000 1.000
X 0.000 0.000 0.500
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 0.600
Y2 0.000 0.000 0.300
W 0.000 0.000 0.000
PSI
Y1 Y2 W
________ ________ ________
Y1 0.500
Y2 0.000 0.500
W 0.000 0.000 0.500
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
________ ________ ________
1.500 1.500 0.000
BETA
Y1 Y2 Z
________ ________ ________
Y1 0.000 0.000 0.300
Y2 0.000 0.000 0.600
Z 0.000 0.000 0.000
PSI
Y1 Y2 Z
________ ________ ________
Y1 0.500
Y2 0.000 0.500
Z 0.000 0.000 0.500
POPULATION 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 0.700
Y2 0.500 0.000 0.000
X 0.000 0.000 0.000
PSI
Y1 Y2 X
________ ________ ________
Y1 1.000
Y2 0.000 1.000
X 0.000 0.000 1.000
POPULATION 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 0.600
Y2 0.000 0.000 0.300
W 0.000 0.000 0.000
PSI
Y1 Y2 W
________ ________ ________
Y1 0.500
Y2 0.000 0.500
W 0.000 0.000 1.000
POPULATION 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
________ ________ ________
1.500 1.500 0.000
BETA
Y1 Y2 Z
________ ________ ________
Y1 0.000 0.000 0.300
Y2 0.000 0.000 0.600
Z 0.000 0.000 0.000
PSI
Y1 Y2 Z
________ ________ ________
Y1 0.500
Y2 0.000 0.500
Z 0.000 0.000 1.000
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
REPLICATION 1:
POTENTIAL PARAMETER WITH
ITERATION SCALE REDUCTION HIGHEST PSR
100 1.943 11
200 1.106 12
300 1.206 12
400 1.618 12
500 2.132 12
600 1.752 12
700 1.235 12
800 1.024 12
900 1.018 12
1000 1.110 12
1100 1.221 12
1200 1.265 12
1300 1.277 12
1400 1.326 12
1500 1.363 11
1600 1.357 11
1700 1.314 11
1800 1.312 11
1900 1.342 11
2000 1.319 11
2100 1.291 11
2200 1.397 11
2300 1.494 11
2400 1.355 11
2500 1.153 11
2600 1.061 11
SAVEDATA INFORMATION
Order of variables
Y1
Y2
X
W
Z
LEVEL2A
LEVEL2B
Save file
ex9.25.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:27:14
Ending Time: 22:27:15
Elapsed Time: 00:00:01
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