Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:31 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a two-level time
series analysis with a univariate first-order autoregressive AR(1) model
for a continuous dependent variable with a covariate, random intercept,
random AR(1) slope, random slope, and random residual variance
DATA: FILE = ex9.31.dat;
VARIABLE: NAMES = y x w xm subject;
WITHIN = x;
BETWEEN = w xm;
CLUSTER = subject;
LAGGED = y(1);
DEFINE: CENTER X (GROUPMEAN);
ANALYSIS: TYPE = TWOLEVEL RANDOM;
ESTIMATOR = BAYES;
PROCESSORS = 2;
BITERATIONS = (2000);
MODEL: %WITHIN%
sy | y ON y&1;
sx | y ON x;
logv | y;
%BETWEEN%
y ON w xm;
sy ON w xm;
sx ON w xm;
logv ON w xm;
y sy sx logv WITH y sy sx logv;
OUTPUT: TECH1 TECH8;
PLOT: TYPE= PLOT3;
INPUT READING TERMINATED NORMALLY
this is an example of a two-level time
series analysis with a univariate first-order autoregressive AR(1) model
for a continuous dependent variable with a covariate, random intercept,
random AR(1) slope, random slope, and random residual variance
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 5000
Number of dependent variables 1
Number of independent variables 4
Number of continuous latent variables 3
Observed dependent variables
Continuous
Y
Observed independent variables
X W XM Y&1
Continuous latent variables
SY SX LOGV
Variables with special functions
Cluster variable SUBJECT
Within variables
X Y&1
Between variables
W XM
Centering (GROUPMEAN)
X
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)
ex9.31.dat
Input data format FREE
SUMMARY OF DATA
Number of clusters 100
Size (s) Cluster ID with Size s
50 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
COVARIANCE COVERAGE OF DATA
Minimum covariance coverage value 0.100
Number of missing data patterns 2
PROPORTION OF DATA PRESENT
Covariance Coverage
Y X W XM
________ ________ ________ ________
Y 1.000
X 1.000 1.000
W 1.000 1.000 1.000
XM 1.000 1.000 1.000 1.000
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
Y 0.013 0.287 -10.377 0.02% -1.551 -0.526 -0.098
5000.000 4.351 1.600 10.792 0.02% 0.390 1.530
X 0.000 0.017 -3.681 0.02% -0.966 -0.305 0.006
5000.000 1.241 -0.140 4.237 0.02% 0.284 0.952
W -0.055 0.514 -2.098 1.00% -0.760 -0.416 -0.285
100.000 0.744 0.072 2.415 1.00% 0.022 0.682
XM 0.136 -0.054 -2.490 1.00% -0.741 -0.031 0.173
100.000 0.963 0.139 2.544 1.00% 0.418 0.829
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 22
Information Criteria
Deviance (DIC) 14729.136
Estimated Number of Parameters (pD) 318.156
MODEL RESULTS
Posterior One-Tailed 95% C.I.
Estimate S.D. P-Value Lower 2.5% Upper 2.5% Significance
Within Level
Between Level
SY ON
W 0.120 0.016 0.000 0.090 0.151 *
XM 0.054 0.014 0.000 0.027 0.082 *
SX ON
W 0.289 0.101 0.004 0.090 0.483 *
XM 0.343 0.089 0.001 0.174 0.519 *
LOGV ON
W 0.325 0.046 0.000 0.234 0.412 *
XM 0.053 0.041 0.086 -0.024 0.137
Y ON
W 0.493 0.092 0.000 0.305 0.666 *
XM 0.392 0.082 0.000 0.236 0.556 *
Y WITH
SY -0.002 0.011 0.401 -0.026 0.020
SX -0.067 0.074 0.157 -0.221 0.070
LOGV -0.006 0.034 0.431 -0.074 0.062
SY WITH
SX -0.009 0.012 0.210 -0.034 0.014
LOGV 0.002 0.006 0.352 -0.009 0.014
SX WITH
LOGV 0.000 0.035 0.495 -0.068 0.067
Intercepts
Y -0.012 0.080 0.444 -0.172 0.145
SY 0.190 0.014 0.000 0.163 0.217 *
SX 0.772 0.086 0.000 0.605 0.939 *
LOGV 0.053 0.039 0.080 -0.022 0.130
Residual Variances
Y 0.592 0.099 0.000 0.433 0.823 *
SY 0.008 0.003 0.000 0.004 0.015 *
SX 0.697 0.114 0.000 0.520 0.957 *
LOGV 0.104 0.023 0.000 0.066 0.155 *
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 0 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 0
X 0 0
Y&1 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN
NU
Y W XM
________ ________ ________
0 0 0
LAMBDA
SY SX 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
SY SX LOGV Y W
________ ________ ________ ________ ________
1 2 3 4 0
ALPHA
XM
________
0
BETA
SY SX LOGV Y W
________ ________ ________ ________ ________
SY 0 0 0 0 5
SX 0 0 0 0 7
LOGV 0 0 0 0 9
Y 0 0 0 0 11
W 0 0 0 0 0
XM 0 0 0 0 0
BETA
XM
________
SY 6
SX 8
LOGV 10
Y 12
W 0
XM 0
PSI
SY SX LOGV Y W
________ ________ ________ ________ ________
SY 13
SX 14 15
LOGV 16 17 18
Y 19 20 21 22
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
________ ________ ________
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 0.000
X 0.000 0.620
Y&1 0.000 0.000 2.175
STARTING VALUES FOR BETWEEN
NU
Y W XM
________ ________ ________
0.000 0.000 0.000
LAMBDA
SY SX 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
SY SX LOGV Y W
________ ________ ________ ________ ________
0.000 0.000 0.000 0.013 0.000
ALPHA
XM
________
0.000
BETA
SY SX LOGV Y W
________ ________ ________ ________ ________
SY 0.000 0.000 0.000 0.000 0.000
SX 0.000 0.000 0.000 0.000 0.000
LOGV 0.000 0.000 0.000 0.000 0.000
Y 0.000 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
XM 0.000 0.000 0.000 0.000 0.000
BETA
XM
________
SY 0.000
SX 0.000
LOGV 0.000
Y 0.000
W 0.000
XM 0.000
PSI
SY SX LOGV Y W
________ ________ ________ ________ ________
SY 1.000
SX 0.000 1.000
LOGV 0.000 0.000 1.000
Y 0.000 0.000 0.000 2.175
W 0.000 0.000 0.000 0.000 0.372
XM 0.000 0.000 0.000 0.000 0.000
PSI
XM
________
XM 0.481
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~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~IW(0.000,-5) infinity infinity infinity
Parameter 14~IW(0.000,-5) infinity infinity infinity
Parameter 15~IW(0.000,-5) infinity infinity infinity
Parameter 16~IW(0.000,-5) infinity infinity infinity
Parameter 17~IW(0.000,-5) infinity infinity infinity
Parameter 18~IW(0.000,-5) infinity infinity infinity
Parameter 19~IW(0.000,-5) infinity infinity infinity
Parameter 20~IW(0.000,-5) infinity infinity infinity
Parameter 21~IW(0.000,-5) infinity infinity infinity
Parameter 22~IW(0.000,-5) 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 1.221 1
200 1.121 5
300 1.028 10
400 1.018 21
500 1.028 17
600 1.014 21
700 1.008 21
800 1.010 16
900 1.017 21
1000 1.024 21
1100 1.012 16
1200 1.010 21
1300 1.011 21
1400 1.006 21
1500 1.003 17
1600 1.003 9
1700 1.009 9
1800 1.008 9
1900 1.007 10
2000 1.004 9
PLOT INFORMATION
The following plots are available:
Histograms (sample values)
Scatterplots (sample values)
Between-level histograms (sample values, sample means/variances)
Between-level scatterplots (sample values, sample means/variances)
Time series plots (sample values, ACF, PACF)
Histogram of subjects per time point
Bayesian posterior parameter distributions
Bayesian posterior parameter trace plots
Bayesian autocorrelation plots
Beginning Time: 23:31:36
Ending Time: 23:31:46
Elapsed Time: 00:00:10
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