Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:35 PM
INPUT INSTRUCTIONS
TITLE: cross-classified regression of y on x with random AR(1),
random intercept, random slope, and random variance
Montecarlo:
names are y x w xm;
nobservations = 20000;
nreps = 1;
CSIZES = 200[100(1)];
ncsize = 1[1];
lagged = y(1);
Between = (level2b)w (level2b)xm;
within = x;
save = ex9.38.dat;
ANALYSIS: TYPE = CROSS random;
estimator=bayes; process=2;
fbiter = (200); ! full convergence not needed for generating the data
model population:
%within%
sx | y ON x;
sy | y ON y&1;
y*1; x*1;
%between LEVEL2A% ! time
y*.5; sx*.2; sy@0;
%between LEVEL2B% ! subject
y*.5; [y*2];
w*1; xm*1;
w with xm*.5;
[sx*.5]; sx*.2;
[sy*.3]; sy*.02;
y on w*.3 xm*.4;
sx on w*.2 xm*.3;
sy on w*.05 xm*.05;
model:
%within%
sx | y ON x;
sy | y ON y&1;
y*1; x*1;
%between LEVEL2A% ! time
y*.5; sx*.2; sy@0; ! random AR over time takes a long time
%between LEVEL2B% ! subject
y*.5; [y*2];
w*1; xm*1;
w with xm*.5;
[sx*.5]; sx*.2;
[sy*.3]; sy*.02;
y on w*.3 xm*.4;
sx on w*.2 xm*.3;
sy on w*.05 xm*.05;
output: tech8 tech9;
INPUT READING TERMINATED NORMALLY
cross-classified regression of y on x with random AR(1),
random intercept, random slope, and random variance
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 20000
Number of replications
Requested 1
Completed 1
Value of seed 0
Number of dependent variables 1
Number of independent variables 4
Number of continuous latent variables 2
Observed dependent variables
Continuous
Y
Observed independent variables
X W XM Y&1
Continuous latent variables
SX SY
Variables with special functions
Within variables
X Y&1
Level 2b between variables
W XM
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)
Fixed number of iterations 200
K-th iteration used for thinning 1
SUMMARY OF DATA FOR THE FIRST REPLICATION
Cluster information
Number of level 2a clusters 100
Number of level 2b clusters 200
MODEL FIT INFORMATION
Number of Free Parameters 22
Information Criteria
Deviance (DIC)
Mean 114463.038
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 114463.038 114463.038
0.980 0.000 114463.038 114463.038
0.950 0.000 114463.038 114463.038
0.900 0.000 114463.038 114463.038
0.800 0.000 114463.038 114463.038
0.700 0.000 114463.038 114463.038
0.500 0.000 114463.038 114463.038
0.300 0.000 114463.038 114463.038
0.200 0.000 114463.038 114463.038
0.100 0.000 114463.038 114463.038
0.050 0.000 114463.038 114463.038
0.020 0.000 114463.038 114463.038
0.010 0.000 114463.038 114463.038
Estimated Number of Parameters (pD)
Mean 760.591
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 760.591 760.591
0.980 0.000 760.591 760.591
0.950 0.000 760.591 760.591
0.900 0.000 760.591 760.591
0.800 0.000 760.591 760.591
0.700 0.000 760.591 760.591
0.500 0.000 760.591 760.591
0.300 0.000 760.591 760.591
0.200 0.000 760.591 760.591
0.100 0.000 760.591 760.591
0.050 0.000 760.591 760.591
0.020 0.000 760.591 760.591
0.010 0.000 760.591 760.591
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Within Level
Means
X 0.000 -0.0038 0.0000 0.0068 0.0000 1.000 0.000
Variances
X 1.000 0.9929 0.0000 0.0091 0.0001 1.000 1.000
Residual Variances
Y 1.000 1.0150 0.0000 0.0100 0.0002 1.000 1.000
Between LEVEL2A Level
Variances
Y 0.500 0.5024 0.0000 0.0700 0.0000 1.000 1.000
SX 0.200 0.1857 0.0000 0.0248 0.0002 1.000 1.000
SY 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Between LEVEL2B Level
SX ON
W 0.200 0.2355 0.0000 0.0350 0.0013 1.000 1.000
XM 0.300 0.2710 0.0000 0.0320 0.0008 1.000 1.000
SY ON
W 0.050 0.0745 0.0000 0.0116 0.0006 0.000 1.000
XM 0.050 0.0346 0.0000 0.0112 0.0002 1.000 1.000
Y ON
W 0.300 0.3186 0.0000 0.0510 0.0003 1.000 1.000
XM 0.400 0.4338 0.0000 0.0547 0.0011 1.000 1.000
W WITH
XM 0.500 0.5761 0.0000 0.0982 0.0058 1.000 1.000
Means
W 0.000 -0.0659 0.0000 0.0814 0.0043 1.000 0.000
XM 0.000 -0.0685 0.0000 0.0808 0.0047 1.000 0.000
Intercepts
Y 2.000 2.0397 0.0000 0.0664 0.0016 1.000 1.000
SX 0.500 0.5650 0.0000 0.0466 0.0042 1.000 1.000
SY 0.300 0.3246 0.0000 0.0111 0.0006 0.000 1.000
Variances
W 1.000 1.1255 0.0000 0.1198 0.0157 1.000 1.000
XM 1.000 1.1720 0.0000 0.1241 0.0296 1.000 1.000
Residual Variances
Y 0.500 0.5223 0.0000 0.0571 0.0005 1.000 1.000
SX 0.200 0.2049 0.0000 0.0199 0.0000 1.000 1.000
SY 0.020 0.0173 0.0000 0.0023 0.0000 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.
SX%2a 0.986 0.000 0.072 0.000
SY%2a 0.000 0.000 0.034 0.000
SX%2b 0.989 0.000 0.098 0.000
SY%2b 0.911 0.000 0.066 0.000
B2a_Y 0.994 0.000 0.081 0.000
B2b_Y 0.988 0.000 0.163 0.000
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
NU
Y X Y&1
________ ________ ________
0 0 0
LAMBDA
Y X Y&1
________ ________ ________
Y 0 0 0
X 0 0 0
Y&1 0 0 0
THETA
Y X Y&1
________ ________ ________
Y 0
X 0 0
Y&1 0 0 0
ALPHA
Y X Y&1
________ ________ ________
0 1 0
BETA
Y X Y&1
________ ________ ________
Y 0 0 0
X 0 0 0
Y&1 0 0 0
PSI
Y X Y&1
________ ________ ________
Y 2
X 0 3
Y&1 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN LEVEL2A
NU
Y
________
0
LAMBDA
SX%2a SY%2a Y
________ ________ ________
Y 0 0 0
THETA
Y
________
Y 0
ALPHA
SX%2a SY%2a Y
________ ________ ________
0 0 0
BETA
SX%2a SY%2a Y
________ ________ ________
SX%2a 0 0 0
SY%2a 0 0 0
Y 0 0 0
PSI
SX%2a SY%2a Y
________ ________ ________
SX%2a 4
SY%2a 0 0
Y 0 0 5
PARAMETER SPECIFICATION FOR BETWEEN LEVEL2B
NU
W XM Y
________ ________ ________
0 0 0
LAMBDA
SX%2b SY%2b W XM Y
________ ________ ________ ________ ________
W 0 0 0 0 0
XM 0 0 0 0 0
Y 0 0 0 0 0
THETA
W XM Y
________ ________ ________
W 0
XM 0 0
Y 0 0 0
ALPHA
SX%2b SY%2b W XM Y
________ ________ ________ ________ ________
6 7 8 9 10
BETA
SX%2b SY%2b W XM Y
________ ________ ________ ________ ________
SX%2b 0 0 11 12 0
SY%2b 0 0 13 14 0
W 0 0 0 0 0
XM 0 0 0 0 0
Y 0 0 15 16 0
PSI
SX%2b SY%2b W XM Y
________ ________ ________ ________ ________
SX%2b 17
SY%2b 0 18
W 0 0 19
XM 0 0 20 21
Y 0 0 0 0 22
STARTING VALUES FOR WITHIN
NU
Y X Y&1
________ ________ ________
0.000 0.000 0.000
LAMBDA
Y X Y&1
________ ________ ________
Y 1.000 0.000 0.000
X 0.000 1.000 0.000
Y&1 0.000 0.000 1.000
THETA
Y X Y&1
________ ________ ________
Y 0.000
X 0.000 0.000
Y&1 0.000 0.000 0.000
ALPHA
Y X Y&1
________ ________ ________
0.000 0.000 0.000
BETA
Y X Y&1
________ ________ ________
Y 0.000 0.000 0.000
X 0.000 0.000 0.000
Y&1 0.000 0.000 0.000
PSI
Y X Y&1
________ ________ ________
Y 1.000
X 0.000 1.000
Y&1 0.000 0.000 0.500
STARTING VALUES FOR BETWEEN LEVEL2A
NU
Y
________
0.000
LAMBDA
SX%2a SY%2a Y
________ ________ ________
Y 0.000 0.000 1.000
THETA
Y
________
Y 0.000
ALPHA
SX%2a SY%2a Y
________ ________ ________
0.000 0.000 0.000
BETA
SX%2a SY%2a Y
________ ________ ________
SX%2a 0.000 0.000 0.000
SY%2a 0.000 0.000 0.000
Y 0.000 0.000 0.000
PSI
SX%2a SY%2a Y
________ ________ ________
SX%2a 0.200
SY%2a 0.000 0.000
Y 0.000 0.000 0.500
STARTING VALUES FOR BETWEEN LEVEL2B
NU
W XM Y
________ ________ ________
0.000 0.000 0.000
LAMBDA
SX%2b SY%2b W XM Y
________ ________ ________ ________ ________
W 0.000 0.000 1.000 0.000 0.000
XM 0.000 0.000 0.000 1.000 0.000
Y 0.000 0.000 0.000 0.000 1.000
THETA
W XM Y
________ ________ ________
W 0.000
XM 0.000 0.000
Y 0.000 0.000 0.000
ALPHA
SX%2b SY%2b W XM Y
________ ________ ________ ________ ________
0.500 0.300 0.000 0.000 2.000
BETA
SX%2b SY%2b W XM Y
________ ________ ________ ________ ________
SX%2b 0.000 0.000 0.200 0.300 0.000
SY%2b 0.000 0.000 0.050 0.050 0.000
W 0.000 0.000 0.000 0.000 0.000
XM 0.000 0.000 0.000 0.000 0.000
Y 0.000 0.000 0.300 0.400 0.000
PSI
SX%2b SY%2b W XM Y
________ ________ ________ ________ ________
SX%2b 0.200
SY%2b 0.000 0.020
W 0.000 0.000 1.000
XM 0.000 0.000 0.500 1.000
Y 0.000 0.000 0.000 0.000 0.500
POPULATION VALUES FOR WITHIN
NU
Y X Y&1
________ ________ ________
0.000 0.000 0.000
LAMBDA
Y X Y&1
________ ________ ________
Y 1.000 0.000 0.000
X 0.000 1.000 0.000
Y&1 0.000 0.000 1.000
THETA
Y X Y&1
________ ________ ________
Y 0.000
X 0.000 0.000
Y&1 0.000 0.000 0.000
ALPHA
Y X Y&1
________ ________ ________
0.000 0.000 0.000
BETA
Y X Y&1
________ ________ ________
Y 0.000 0.000 0.000
X 0.000 0.000 0.000
Y&1 0.000 0.000 0.000
PSI
Y X Y&1
________ ________ ________
Y 1.000
X 0.000 1.000
Y&1 0.000 0.000 1.000
POPULATION VALUES FOR BETWEEN LEVEL2A
NU
Y
________
0.000
LAMBDA
SX%2a SY%2a Y
________ ________ ________
Y 0.000 0.000 1.000
THETA
Y
________
Y 0.000
ALPHA
SX%2a SY%2a Y
________ ________ ________
0.000 0.000 0.000
BETA
SX%2a SY%2a Y
________ ________ ________
SX%2a 0.000 0.000 0.000
SY%2a 0.000 0.000 0.000
Y 0.000 0.000 0.000
PSI
SX%2a SY%2a Y
________ ________ ________
SX%2a 0.200
SY%2a 0.000 0.000
Y 0.000 0.000 0.500
POPULATION VALUES FOR BETWEEN LEVEL2B
NU
W XM Y
________ ________ ________
0.000 0.000 0.000
LAMBDA
SX%2b SY%2b W XM Y
________ ________ ________ ________ ________
W 0.000 0.000 1.000 0.000 0.000
XM 0.000 0.000 0.000 1.000 0.000
Y 0.000 0.000 0.000 0.000 1.000
THETA
W XM Y
________ ________ ________
W 0.000
XM 0.000 0.000
Y 0.000 0.000 0.000
ALPHA
SX%2b SY%2b W XM Y
________ ________ ________ ________ ________
0.500 0.300 0.000 0.000 2.000
BETA
SX%2b SY%2b W XM Y
________ ________ ________ ________ ________
SX%2b 0.000 0.000 0.200 0.300 0.000
SY%2b 0.000 0.000 0.050 0.050 0.000
W 0.000 0.000 0.000 0.000 0.000
XM 0.000 0.000 0.000 0.000 0.000
Y 0.000 0.000 0.300 0.400 0.000
PSI
SX%2b SY%2b W XM Y
________ ________ ________ ________ ________
SX%2b 0.200
SY%2b 0.000 0.020
W 0.000 0.000 1.000
XM 0.000 0.000 0.500 1.000
Y 0.000 0.000 0.000 0.000 0.500
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~IG(-1.000,0.000) infinity 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~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~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~N(0.000,infinity) 0.0000 infinity infinity
Parameter 16~N(0.000,infinity) 0.0000 infinity infinity
Parameter 17~IG(-1.000,0.000) infinity infinity infinity
Parameter 18~IG(-1.000,0.000) infinity infinity infinity
Parameter 19~IW(0.000,-3) infinity infinity infinity
Parameter 20~IW(0.000,-3) infinity infinity infinity
Parameter 21~IW(0.000,-3) infinity infinity infinity
Parameter 22~IG(-1.000,0.000) 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 1.372 6
200 1.045 13
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
W
XM
Y
X
LEVEL2A
LEVEL2B
Y&1
Save file
ex9.38.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:35:16
Ending Time: 22:36:54
Elapsed Time: 00:01:38
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