Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:30 PM
INPUT INSTRUCTIONS
Title: two-level reg of y on x with random AR(1),
random intercept, random slope, and random variance
MONTECARLO: NAMES ARE y x w xm;
NOBS = 5000;
NREP = 1;
NCSIZES = 1;
CSIZES = 100(50);
lagged = y(1) x(1);
within = x;
between = w xm;
save = ex9.31.dat;
ANALYSIS: TYPE = TWOLEVEL RANDOM;
estimator=bayes;
proc=2;
biter=(1000);
MODEL POPULATION:
%WITHIN%
x*1;
sx | y on x;
sy | y on y&1;
logv | y;
x on x&1*.5;
%BETWEEN%
w-xm*1;
[sx*.7]; [sy*.2]; [logv*0];
y*0.3; sx*0.5; sy*.01; logv*.1;
y on w*.5 xm*.3;
sy on w*.1 xm*.05;
sx on w*.3 xm*.4;
logv on w*.3 xm*.1;
MODEL:
%WITHIN%
x*1;
sx | y on x;
sy | y on y&1;
logv | y;
x on x&1*.5;
%BETWEEN%
[sx*.7]; [sy*.2]; [logv*0];
y*0.3; sx*0.5; sy*.01; logv*.1;
y on w*.5 xm*.3;
sy on w*.1 xm*.05;
sx on w*.3 xm*.4;
logv on w*.3 xm*.1;
output:
tech8;
INPUT READING TERMINATED NORMALLY
two-level reg 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 5000
Number of replications
Requested 1
Completed 1
Value of seed 0
Number of dependent variables 2
Number of independent variables 4
Number of continuous latent variables 3
Observed dependent variables
Continuous
Y X
Observed independent variables
W XM Y&1 X&1
Continuous latent variables
SX SY LOGV
Variables with special functions
Within variables
X Y&1 X&1
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)
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
Size (s) Number of clusters of Size s
50 100
MODEL FIT INFORMATION
Number of Free Parameters 19
Information Criteria
Deviance (DIC)
Mean 28942.243
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 28942.243 28942.243
0.980 0.000 28942.243 28942.243
0.950 0.000 28942.243 28942.243
0.900 0.000 28942.243 28942.243
0.800 0.000 28942.243 28942.243
0.700 0.000 28942.243 28942.243
0.500 0.000 28942.243 28942.243
0.300 0.000 28942.243 28942.243
0.200 0.000 28942.243 28942.243
0.100 0.000 28942.243 28942.243
0.050 0.000 28942.243 28942.243
0.020 0.000 28942.243 28942.243
0.010 0.000 28942.243 28942.243
Estimated Number of Parameters (pD)
Mean 332.607
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 332.607 332.607
0.980 0.000 332.607 332.607
0.950 0.000 332.607 332.607
0.900 0.000 332.607 332.607
0.800 0.000 332.607 332.607
0.700 0.000 332.607 332.607
0.500 0.000 332.607 332.607
0.300 0.000 332.607 332.607
0.200 0.000 332.607 332.607
0.100 0.000 332.607 332.607
0.050 0.000 332.607 332.607
0.020 0.000 332.607 332.607
0.010 0.000 332.607 332.607
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Within Level
X ON
X&1 0.500 0.4885 0.0000 0.0123 0.0001 1.000 1.000
Intercepts
X 0.000 0.0135 0.0000 0.0144 0.0002 1.000 0.000
Residual Variances
X 1.000 1.0014 0.0000 0.0206 0.0000 1.000 1.000
Between Level
SY ON
W 0.100 0.1189 0.0000 0.0151 0.0004 1.000 1.000
XM 0.050 0.0522 0.0000 0.0137 0.0000 1.000 1.000
SX ON
W 0.300 0.2939 0.0000 0.0942 0.0000 1.000 1.000
XM 0.400 0.3489 0.0000 0.0829 0.0026 1.000 1.000
LOGV ON
W 0.300 0.3266 0.0000 0.0445 0.0007 1.000 1.000
XM 0.100 0.0539 0.0000 0.0382 0.0021 1.000 0.000
Y ON
W 0.500 0.4848 0.0000 0.0787 0.0002 1.000 1.000
XM 0.300 0.2931 0.0000 0.0662 0.0000 1.000 1.000
Intercepts
Y 0.000 -0.0216 0.0000 0.0661 0.0005 1.000 0.000
SX 0.700 0.7716 0.0000 0.0827 0.0051 1.000 1.000
SY 0.200 0.1884 0.0000 0.0131 0.0001 1.000 1.000
LOGV 0.000 0.0566 0.0000 0.0400 0.0032 1.000 0.000
Residual Variances
Y 0.300 0.3767 0.0000 0.0614 0.0059 1.000 1.000
SX 0.500 0.6516 0.0000 0.0998 0.0230 1.000 1.000
SY 0.010 0.0075 0.0000 0.0021 0.0000 1.000 1.000
LOGV 0.100 0.0950 0.0000 0.0214 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 0.987 0.000 0.140 0.000
SY 0.824 0.000 0.080 0.000
LOGV 0.894 0.000 0.183 0.000
Y 0.979 0.000 0.159 0.000
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
NU
Y X Y&1 X&1
________ ________ ________ ________
0 0 0 0
LAMBDA
Y X Y&1 X&1
________ ________ ________ ________
Y 0 0 0 0
X 0 0 0 0
Y&1 0 0 0 0
X&1 0 0 0 0
THETA
Y X Y&1 X&1
________ ________ ________ ________
Y 0
X 0 0
Y&1 0 0 0
X&1 0 0 0 0
ALPHA
Y X Y&1 X&1
________ ________ ________ ________
0 1 0 0
BETA
Y X Y&1 X&1
________ ________ ________ ________
Y 0 0 0 0
X 0 0 0 2
Y&1 0 0 0 0
X&1 0 0 0 0
PSI
Y X Y&1 X&1
________ ________ ________ ________
Y 0
X 0 3
Y&1 0 0 0
X&1 0 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN
NU
Y W XM
________ ________ ________
0 0 0
LAMBDA
SX SY LOGV Y W
________ ________ ________ ________ ________
Y 0 0 0 0 0
W 0 0 0 0 0
XM 0 0 0 0 0
LAMBDA
XM
________
Y 0
W 0
XM 0
THETA
Y W XM
________ ________ ________
Y 0
W 0 0
XM 0 0 0
ALPHA
SX SY LOGV Y W
________ ________ ________ ________ ________
4 5 6 7 0
ALPHA
XM
________
0
BETA
SX SY LOGV Y W
________ ________ ________ ________ ________
SX 0 0 0 0 8
SY 0 0 0 0 10
LOGV 0 0 0 0 12
Y 0 0 0 0 14
W 0 0 0 0 0
XM 0 0 0 0 0
BETA
XM
________
SX 9
SY 11
LOGV 13
Y 15
W 0
XM 0
PSI
SX SY LOGV Y W
________ ________ ________ ________ ________
SX 16
SY 0 17
LOGV 0 0 18
Y 0 0 0 19
W 0 0 0 0 0
XM 0 0 0 0 0
PSI
XM
________
XM 0
STARTING VALUES FOR WITHIN
NU
Y X Y&1 X&1
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
Y X Y&1 X&1
________ ________ ________ ________
Y 1.000 0.000 0.000 0.000
X 0.000 1.000 0.000 0.000
Y&1 0.000 0.000 1.000 0.000
X&1 0.000 0.000 0.000 1.000
THETA
Y X Y&1 X&1
________ ________ ________ ________
Y 0.000
X 0.000 0.000
Y&1 0.000 0.000 0.000
X&1 0.000 0.000 0.000 0.000
ALPHA
Y X Y&1 X&1
________ ________ ________ ________
0.000 0.000 0.000 0.000
BETA
Y X Y&1 X&1
________ ________ ________ ________
Y 0.000 0.000 0.000 0.000
X 0.000 0.000 0.000 0.500
Y&1 0.000 0.000 0.000 0.000
X&1 0.000 0.000 0.000 0.000
PSI
Y X Y&1 X&1
________ ________ ________ ________
Y 0.000
X 0.000 1.000
Y&1 0.000 0.000 0.500
X&1 0.000 0.000 0.000 0.500
STARTING VALUES FOR BETWEEN
NU
Y W XM
________ ________ ________
0.000 0.000 0.000
LAMBDA
SX SY LOGV Y W
________ ________ ________ ________ ________
Y 0.000 0.000 0.000 1.000 0.000
W 0.000 0.000 0.000 0.000 1.000
XM 0.000 0.000 0.000 0.000 0.000
LAMBDA
XM
________
Y 0.000
W 0.000
XM 1.000
THETA
Y W XM
________ ________ ________
Y 0.000
W 0.000 0.000
XM 0.000 0.000 0.000
ALPHA
SX SY LOGV Y W
________ ________ ________ ________ ________
0.700 0.200 0.000 0.000 0.000
ALPHA
XM
________
0.000
BETA
SX SY LOGV Y W
________ ________ ________ ________ ________
SX 0.000 0.000 0.000 0.000 0.300
SY 0.000 0.000 0.000 0.000 0.100
LOGV 0.000 0.000 0.000 0.000 0.300
Y 0.000 0.000 0.000 0.000 0.500
W 0.000 0.000 0.000 0.000 0.000
XM 0.000 0.000 0.000 0.000 0.000
BETA
XM
________
SX 0.400
SY 0.050
LOGV 0.100
Y 0.300
W 0.000
XM 0.000
PSI
SX SY LOGV Y W
________ ________ ________ ________ ________
SX 0.500
SY 0.000 0.010
LOGV 0.000 0.000 0.100
Y 0.000 0.000 0.000 0.300
W 0.000 0.000 0.000 0.000 0.500
XM 0.000 0.000 0.000 0.000 0.000
PSI
XM
________
XM 0.500
POPULATION VALUES FOR WITHIN
NU
Y X Y&1 X&1
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
Y X Y&1 X&1
________ ________ ________ ________
Y 1.000 0.000 0.000 0.000
X 0.000 1.000 0.000 0.000
Y&1 0.000 0.000 1.000 0.000
X&1 0.000 0.000 0.000 1.000
THETA
Y X Y&1 X&1
________ ________ ________ ________
Y 0.000
X 0.000 0.000
Y&1 0.000 0.000 0.000
X&1 0.000 0.000 0.000 0.000
ALPHA
Y X Y&1 X&1
________ ________ ________ ________
0.000 0.000 0.000 0.000
BETA
Y X Y&1 X&1
________ ________ ________ ________
Y 0.000 0.000 0.000 0.000
X 0.000 0.000 0.000 0.500
Y&1 0.000 0.000 0.000 0.000
X&1 0.000 0.000 0.000 0.000
PSI
Y X Y&1 X&1
________ ________ ________ ________
Y 0.000
X 0.000 1.000
Y&1 0.000 0.000 1.000
X&1 0.000 0.000 0.000 1.000
POPULATION VALUES FOR BETWEEN
NU
Y W XM
________ ________ ________
0.000 0.000 0.000
LAMBDA
SX SY LOGV Y W
________ ________ ________ ________ ________
Y 0.000 0.000 0.000 1.000 0.000
W 0.000 0.000 0.000 0.000 1.000
XM 0.000 0.000 0.000 0.000 0.000
LAMBDA
XM
________
Y 0.000
W 0.000
XM 1.000
THETA
Y W XM
________ ________ ________
Y 0.000
W 0.000 0.000
XM 0.000 0.000 0.000
ALPHA
SX SY LOGV Y W
________ ________ ________ ________ ________
0.700 0.200 0.000 0.000 0.000
ALPHA
XM
________
0.000
BETA
SX SY LOGV Y W
________ ________ ________ ________ ________
SX 0.000 0.000 0.000 0.000 0.300
SY 0.000 0.000 0.000 0.000 0.100
LOGV 0.000 0.000 0.000 0.000 0.300
Y 0.000 0.000 0.000 0.000 0.500
W 0.000 0.000 0.000 0.000 0.000
XM 0.000 0.000 0.000 0.000 0.000
BETA
XM
________
SX 0.400
SY 0.050
LOGV 0.100
Y 0.300
W 0.000
XM 0.000
PSI
SX SY LOGV Y W
________ ________ ________ ________ ________
SX 0.500
SY 0.000 0.010
LOGV 0.000 0.000 0.100
Y 0.000 0.000 0.000 0.300
W 0.000 0.000 0.000 0.000 1.000
XM 0.000 0.000 0.000 0.000 0.000
PSI
XM
________
XM 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~IG(-1.000,0.000) infinity infinity infinity
Parameter 4~N(0.000,infinity) 0.0000 infinity infinity
Parameter 5~N(0.000,infinity) 0.0000 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~IG(-1.000,0.000) infinity infinity infinity
Parameter 17~IG(-1.000,0.000) infinity infinity infinity
Parameter 18~IG(-1.000,0.000) infinity infinity infinity
Parameter 19~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 1.113 6
200 1.037 13
300 1.068 11
400 1.081 11
500 1.024 18
600 1.021 13
700 1.014 11
800 1.009 12
900 1.008 12
1000 1.006 12
SAVEDATA INFORMATION
Order of variables
Y
X
W
XM
CLUSTER
Y&1
X&1
Save file
ex9.31.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:30:15
Ending Time: 22:30:21
Elapsed Time: 00:00:06
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