Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:33 PM
INPUT INSTRUCTIONS
TITLE: two-level time series analysis with a univariate first-order autoregressive AR
for a continuous dependent variable with a covariate, linear trend, random slopes
and a random residual variance
Set up as a cross-classified model with empty Level2A (time) model
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 = ex9.37.dat;
ANALYSIS: TYPE = CROSS random;
estimator=bayes; process=2;
fbiter = (100); ! doesn't need to go to convergence to generate the data
model population:
%within%
sx | y ON x;
sy | y ON y&1;
y*1; x*1;
%between LEVEL2A% ! time
! empty
y@0; sx@0; 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
! empty
y@0; sx@0; sy@0;
%between LEVEL2B% ! subject
y*.5; [y*2];
[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;
*** WARNING
Input line exceeded 90 characters. Some input may be truncated.
TITLE: two-level time series analysis with a univariate first-order autoregressive AR(
*** WARNING
Input line exceeded 90 characters. Some input may be truncated.
for a continuous dependent variable with a covariate, linear trend, random slopes,
2 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
two-level time series analysis with a univariate first-order autoregressive AR(
for a continuous dependent variable with a covariate, linear trend, random slopes
and a random residual variance
Set up as a cross-classified model with empty Level2A (time) model
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 100
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 15
Information Criteria
Deviance (DIC)
Mean 114255.205
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 114255.205 114255.205
0.980 0.000 114255.205 114255.205
0.950 0.000 114255.205 114255.205
0.900 0.000 114255.205 114255.205
0.800 0.000 114255.205 114255.205
0.700 0.000 114255.205 114255.205
0.500 0.000 114255.205 114255.205
0.300 0.000 114255.205 114255.205
0.200 0.000 114255.205 114255.205
0.100 0.000 114255.205 114255.205
0.050 0.000 114255.205 114255.205
0.020 0.000 114255.205 114255.205
0.010 0.000 114255.205 114255.205
Estimated Number of Parameters (pD)
Mean 563.322
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 563.322 563.322
0.980 0.000 563.322 563.322
0.950 0.000 563.322 563.322
0.900 0.000 563.322 563.322
0.800 0.000 563.322 563.322
0.700 0.000 563.322 563.322
0.500 0.000 563.322 563.322
0.300 0.000 563.322 563.322
0.200 0.000 563.322 563.322
0.100 0.000 563.322 563.322
0.050 0.000 563.322 563.322
0.020 0.000 563.322 563.322
0.010 0.000 563.322 563.322
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Within Level
Means
X 0.000 -0.0041 0.0000 0.0071 0.0000 1.000 0.000
Variances
X 1.000 0.9913 0.0000 0.0096 0.0001 1.000 1.000
Residual Variances
Y 1.000 1.0182 0.0000 0.0096 0.0003 1.000 1.000
Between LEVEL2A Level
Variances
Y 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
SX 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
SY 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Between LEVEL2B Level
SX ON
W 0.200 0.2360 0.0000 0.0366 0.0013 1.000 1.000
XM 0.300 0.2726 0.0000 0.0372 0.0008 1.000 1.000
SY ON
W 0.050 0.0739 0.0000 0.0115 0.0006 1.000 1.000
XM 0.050 0.0309 0.0000 0.0118 0.0004 1.000 1.000
Y ON
W 0.300 0.3213 0.0000 0.0559 0.0005 1.000 1.000
XM 0.400 0.4354 0.0000 0.0609 0.0012 1.000 1.000
Intercepts
Y 2.000 2.0022 0.0000 0.0523 0.0000 1.000 1.000
SX 0.500 0.5225 0.0000 0.0344 0.0005 1.000 1.000
SY 0.300 0.3244 0.0000 0.0101 0.0006 0.000 1.000
Residual Variances
Y 0.500 0.5256 0.0000 0.0553 0.0007 1.000 1.000
SX 0.200 0.2033 0.0000 0.0207 0.0000 1.000 1.000
SY 0.020 0.0170 0.0000 0.0022 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 0.000 0.000 0.029 0.000
SY%2a 0.000 0.000 0.034 0.000
SX%2b 0.989 0.000 0.099 0.000
SY%2b 0.904 0.000 0.069 0.000
B2a_Y 0.438 0.000 0.028 0.000
B2b_Y 0.988 0.000 0.154 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 0
SY%2a 0 0
Y 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN LEVEL2B
NU
Y W XM
________ ________ ________
0 0 0
LAMBDA
SX%2b SY%2b Y W XM
________ ________ ________ ________ ________
Y 0 0 0 0 0
W 0 0 0 0 0
XM 0 0 0 0 0
THETA
Y W XM
________ ________ ________
Y 0
W 0 0
XM 0 0 0
ALPHA
SX%2b SY%2b Y W XM
________ ________ ________ ________ ________
4 5 6 0 0
BETA
SX%2b SY%2b Y W XM
________ ________ ________ ________ ________
SX%2b 0 0 0 7 8
SY%2b 0 0 0 9 10
Y 0 0 0 11 12
W 0 0 0 0 0
XM 0 0 0 0 0
PSI
SX%2b SY%2b Y W XM
________ ________ ________ ________ ________
SX%2b 13
SY%2b 0 14
Y 0 0 15
W 0 0 0 0
XM 0 0 0 0 0
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 0.000
SY%2a 0.000 0.000
Y 0.000 0.000 0.000
STARTING VALUES FOR BETWEEN LEVEL2B
NU
Y W XM
________ ________ ________
0.000 0.000 0.000
LAMBDA
SX%2b SY%2b Y W XM
________ ________ ________ ________ ________
Y 0.000 0.000 1.000 0.000 0.000
W 0.000 0.000 0.000 1.000 0.000
XM 0.000 0.000 0.000 0.000 1.000
THETA
Y W XM
________ ________ ________
Y 0.000
W 0.000 0.000
XM 0.000 0.000 0.000
ALPHA
SX%2b SY%2b Y W XM
________ ________ ________ ________ ________
0.500 0.300 2.000 0.000 0.000
BETA
SX%2b SY%2b Y W XM
________ ________ ________ ________ ________
SX%2b 0.000 0.000 0.000 0.200 0.300
SY%2b 0.000 0.000 0.000 0.050 0.050
Y 0.000 0.000 0.000 0.300 0.400
W 0.000 0.000 0.000 0.000 0.000
XM 0.000 0.000 0.000 0.000 0.000
PSI
SX%2b SY%2b Y W XM
________ ________ ________ ________ ________
SX%2b 0.200
SY%2b 0.000 0.020
Y 0.000 0.000 0.500
W 0.000 0.000 0.000 0.500
XM 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 0.000
SY%2a 0.000 0.000
Y 0.000 0.000 0.000
POPULATION VALUES FOR BETWEEN LEVEL2B
NU
Y W XM
________ ________ ________
0.000 0.000 0.000
LAMBDA
SX%2b SY%2b Y W XM
________ ________ ________ ________ ________
Y 0.000 0.000 1.000 0.000 0.000
W 0.000 0.000 0.000 1.000 0.000
XM 0.000 0.000 0.000 0.000 1.000
THETA
Y W XM
________ ________ ________
Y 0.000
W 0.000 0.000
XM 0.000 0.000 0.000
ALPHA
SX%2b SY%2b Y W XM
________ ________ ________ ________ ________
0.500 0.300 2.000 0.000 0.000
BETA
SX%2b SY%2b Y W XM
________ ________ ________ ________ ________
SX%2b 0.000 0.000 0.000 0.200 0.300
SY%2b 0.000 0.000 0.000 0.050 0.050
Y 0.000 0.000 0.000 0.300 0.400
W 0.000 0.000 0.000 0.000 0.000
XM 0.000 0.000 0.000 0.000 0.000
PSI
SX%2b SY%2b Y W XM
________ ________ ________ ________ ________
SX%2b 0.200
SY%2b 0.000 0.020
Y 0.000 0.000 0.500
W 0.000 0.000 0.000 1.000
XM 0.000 0.000 0.000 0.500 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~IG(-1.000,0.000) infinity 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~IG(-1.000,0.000) infinity infinity infinity
Parameter 14~IG(-1.000,0.000) infinity infinity infinity
Parameter 15~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 1.118 6
200 1.009 2
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
Y
X
W
XM
LEVEL2A
LEVEL2B
Y&1
Save file
ex9.37.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:33:35
Ending Time: 22:35:16
Elapsed Time: 00:01:41
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