Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:49 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a cross-classified time series analysis
with a univariate first-order autoregressive AR(1) model for a
continuous dependent variable with a covariate, linear trend, and random slope
DATA: FILE = ex9.39.dat;
VARIABLE: NAMES = w xm y x time subject;
USEVARIABLES = w xm y x timew timet;
WITHIN = x timew;
BETWEEN = (subject) w xm (time) timet;
CLUSTER = subject time;
LAGGED = y(1);
DEFINE: timew = time;
timet = time;
ANALYSIS: TYPE = CROSSCLASSIFIED RANDOM;
ESTIMATOR = BAYES;
PROCESSORS = 2;
!BITERATIONS = (5000);
FBITERATIONS = 100;
MODEL: %WITHIN%
sy | y ON y&1;
s | y ON timew;
sx | y ON x;
logv | y;
%BETWEEN subject%
y sy sx logv s ON w xm;
y sy sx logv s WITH y sy s logv s;
%BETWEEN time%
sx ON timet;
y sy sx WITH y sy sx;
s@0;
OUTPUT: TECH1 TECH8;
PLOT: TYPE = PLOT3;
INPUT READING TERMINATED NORMALLY
this is an example of a cross-classified time series analysis
with a univariate first-order autoregressive AR(1) model for a
continuous dependent variable with a covariate, linear trend, and random slope
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 20000
Number of dependent variables 1
Number of independent variables 6
Number of continuous latent variables 4
Observed dependent variables
Continuous
Y
Observed independent variables
W XM X TIMEW TIMET Y&1
Continuous latent variables
SY S SX LOGV
Variables with special functions
Cluster variables SUBJECT TIME
Within variables
X TIMEW Y&1
Level 2a between variables
TIMET
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
Input data file(s)
ex9.39.dat
Input data format FREE
SUMMARY OF DATA
Cluster information for SUBJECT
Number of clusters 200
Size (s) Cluster ID with Size s
100 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 99 100 101 102 103 104 105 106 107 108
109 110 111 112 113 114 115 116 117 118 119 120 121
122 123 124 125 126 127 128 129 130 131 132 133 134
135 136 137 138 139 140 141 142 143 144 145 146 147
148 149 150 151 152 153 154 155 156 157 158 159 160
161 162 163 164 165 166 167 168 169 170 171 172 173
174 175 176 177 178 179 180 181 182 183 184 185 186
187 188 189 190 191 192 193 194 195 196 197 198 199
200
COVARIANCE COVERAGE OF DATA
Minimum covariance coverage value 0.100
Number of missing data patterns 2
PROPORTION OF DATA PRESENT
Covariance Coverage
Y X TIMEW W XM
________ ________ ________ ________ ________
Y 1.000
X 1.000 1.000
TIMEW 1.000 1.000 1.000
W 1.000 1.000 1.000 1.000
XM 1.000 1.000 1.000 1.000 1.000
TIMET 1.000 1.000 1.000 1.000 1.000
Covariance Coverage
TIMET
________
TIMET 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 1.999 0.212 -5.895 0.01% 0.404 1.482 1.950
20000.000 3.664 0.438 12.588 0.01% 2.407 3.567
X -0.004 0.031 -3.748 0.01% -0.848 -0.258 -0.008
20000.000 0.992 -0.011 3.770 0.01% 0.244 0.832
TIMEW 50.500 0.000 1.000 1.00% 20.000 40.000 50.500
20000.000 833.250 -1.200 100.000 1.00% 60.000 80.000
W -0.067 0.070 -2.681 0.50% -1.046 -0.386 -0.059
200.000 1.094 -0.509 2.781 0.50% 0.307 0.862
XM -0.059 -0.029 -3.062 0.50% -1.004 -0.326 0.019
200.000 1.132 0.216 3.251 0.50% 0.247 0.723
TIMET 50.500 0.000 1.000 1.00% 20.000 40.000 50.500
100.000 833.250 -1.200 100.000 1.00% 60.000 80.000
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 37
Information Criteria
Deviance (DIC) 57883.887
Estimated Number of Parameters (pD) 874.685
MODEL RESULTS
Posterior One-Tailed 95% C.I.
Estimate S.D. P-Value Lower 2.5% Upper 2.5% Significance
Within Level
Between TIME Level
SX ON
TIMET 0.000 0.001 0.490 -0.002 0.003
Y WITH
SY 0.007 0.005 0.070 -0.003 0.018
SX -0.015 0.036 0.300 -0.087 0.051
SY WITH
SX 0.000 0.003 0.495 -0.006 0.006
Variances
Y 0.541 0.083 0.000 0.398 0.743 *
SY 0.002 0.001 0.000 0.001 0.004 *
S 0.000 0.000 0.000 0.000 0.000
Residual Variances
SX 0.198 0.032 0.000 0.142 0.268 *
Between SUBJECT Level
SY ON
W 0.076 0.012 0.000 0.054 0.096 *
XM 0.034 0.013 0.000 0.009 0.057 *
SX ON
W 0.232 0.036 0.000 0.161 0.304 *
XM 0.275 0.034 0.000 0.194 0.336 *
LOGV ON
W 0.006 0.011 0.385 -0.013 0.022
XM -0.013 0.008 0.045 -0.028 0.001
S ON
W 0.000 0.000 0.090 -0.001 0.000
XM 0.000 0.000 0.030 0.000 0.001
Y ON
W 0.346 0.068 0.000 0.204 0.491 *
XM 0.406 0.063 0.000 0.288 0.515 *
Y WITH
SY -0.010 0.010 0.170 -0.028 0.011
S 0.000 0.000 0.000 -0.001 0.000 *
LOGV 0.013 0.007 0.090 -0.006 0.022
SX 0.003 0.032 0.465 -0.057 0.061
SY WITH
S 0.000 0.000 0.490 0.000 0.000
LOGV -0.002 0.001 0.020 -0.004 0.000 *
SX 0.000 0.005 0.475 -0.010 0.011
SX WITH
S 0.000 0.000 0.085 0.000 0.000
LOGV 0.002 0.003 0.295 -0.004 0.008
LOGV WITH
S 0.000 0.000 0.215 0.000 0.000
Intercepts
Y 2.062 0.092 0.000 1.881 2.218 *
SY 0.332 0.013 0.000 0.308 0.351 *
S 0.000 0.001 0.315 -0.001 0.002
SX 0.573 0.070 0.000 0.423 0.675 *
LOGV 0.014 0.008 0.020 0.000 0.029 *
Residual Variances
Y 0.603 0.074 0.000 0.471 0.784 *
SY 0.018 0.002 0.000 0.014 0.024 *
S 0.000 0.000 0.000 0.000 0.000 *
SX 0.210 0.022 0.000 0.171 0.257 *
LOGV 0.002 0.000 0.000 0.001 0.003 *
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
NU
Y X TIMEW Y&1
________ ________ ________ ________
0 0 0 0
LAMBDA
Y X TIMEW Y&1
________ ________ ________ ________
Y 0 0 0 0
X 0 0 0 0
TIMEW 0 0 0 0
Y&1 0 0 0 0
THETA
Y X TIMEW Y&1
________ ________ ________ ________
Y 0
X 0 0
TIMEW 0 0 0
Y&1 0 0 0 0
ALPHA
Y X TIMEW Y&1
________ ________ ________ ________
0 0 0 0
BETA
Y X TIMEW Y&1
________ ________ ________ ________
Y 0 0 0 0
X 0 0 0 0
TIMEW 0 0 0 0
Y&1 0 0 0 0
PSI
Y X TIMEW Y&1
________ ________ ________ ________
Y 0
X 0 0
TIMEW 0 0 0
Y&1 0 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN TIME
NU
Y TIMET
________ ________
0 0
LAMBDA
SY%2a S%2a SX%2a LOGV%2a Y
________ ________ ________ ________ ________
Y 0 0 0 0 0
TIMET 0 0 0 0 0
LAMBDA
TIMET
________
Y 0
TIMET 0
THETA
Y TIMET
________ ________
Y 0
TIMET 0 0
ALPHA
SY%2a S%2a SX%2a LOGV%2a Y
________ ________ ________ ________ ________
0 0 0 0 0
ALPHA
TIMET
________
0
BETA
SY%2a S%2a SX%2a LOGV%2a Y
________ ________ ________ ________ ________
SY%2a 0 0 0 0 0
S%2a 0 0 0 0 0
SX%2a 0 0 0 0 0
LOGV%2a 0 0 0 0 0
Y 0 0 0 0 0
TIMET 0 0 0 0 0
BETA
TIMET
________
SY%2a 0
S%2a 0
SX%2a 1
LOGV%2a 0
Y 0
TIMET 0
PSI
SY%2a S%2a SX%2a LOGV%2a Y
________ ________ ________ ________ ________
SY%2a 2
S%2a 0 0
SX%2a 3 0 4
LOGV%2a 0 0 0 0
Y 5 0 6 0 7
TIMET 0 0 0 0 0
PSI
TIMET
________
TIMET 0
PARAMETER SPECIFICATION FOR BETWEEN SUBJECT
NU
Y W XM
________ ________ ________
0 0 0
LAMBDA
SY%2b S%2b SX%2b LOGV%2b Y
________ ________ ________ ________ ________
Y 0 0 0 0 0
W 0 0 0 0 0
XM 0 0 0 0 0
LAMBDA
W XM
________ ________
Y 0 0
W 0 0
XM 0 0
THETA
Y W XM
________ ________ ________
Y 0
W 0 0
XM 0 0 0
ALPHA
SY%2b S%2b SX%2b LOGV%2b Y
________ ________ ________ ________ ________
8 9 10 11 12
ALPHA
W XM
________ ________
0 0
BETA
SY%2b S%2b SX%2b LOGV%2b Y
________ ________ ________ ________ ________
SY%2b 0 0 0 0 0
S%2b 0 0 0 0 0
SX%2b 0 0 0 0 0
LOGV%2b 0 0 0 0 0
Y 0 0 0 0 0
W 0 0 0 0 0
XM 0 0 0 0 0
BETA
W XM
________ ________
SY%2b 13 14
S%2b 15 16
SX%2b 17 18
LOGV%2b 19 20
Y 21 22
W 0 0
XM 0 0
PSI
SY%2b S%2b SX%2b LOGV%2b Y
________ ________ ________ ________ ________
SY%2b 23
S%2b 24 25
SX%2b 26 27 28
LOGV%2b 29 30 31 32
Y 33 34 35 36 37
W 0 0 0 0 0
XM 0 0 0 0 0
PSI
W XM
________ ________
W 0
XM 0 0
STARTING VALUES FOR WITHIN
NU
Y X TIMEW Y&1
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
Y X TIMEW Y&1
________ ________ ________ ________
Y 1.000 0.000 0.000 0.000
X 0.000 1.000 0.000 0.000
TIMEW 0.000 0.000 1.000 0.000
Y&1 0.000 0.000 0.000 1.000
THETA
Y X TIMEW Y&1
________ ________ ________ ________
Y 0.000
X 0.000 0.000
TIMEW 0.000 0.000 0.000
Y&1 0.000 0.000 0.000 0.000
ALPHA
Y X TIMEW Y&1
________ ________ ________ ________
0.000 0.000 0.000 0.000
BETA
Y X TIMEW Y&1
________ ________ ________ ________
Y 0.000 0.000 0.000 0.000
X 0.000 0.000 0.000 0.000
TIMEW 0.000 0.000 0.000 0.000
Y&1 0.000 0.000 0.000 0.000
PSI
Y X TIMEW Y&1
________ ________ ________ ________
Y 0.000
X 0.000 0.496
TIMEW 0.000 0.000 416.625
Y&1 0.000 0.000 0.000 1.836
STARTING VALUES FOR BETWEEN TIME
NU
Y TIMET
________ ________
0.000 0.000
LAMBDA
SY%2a S%2a SX%2a LOGV%2a Y
________ ________ ________ ________ ________
Y 0.000 0.000 0.000 0.000 1.000
TIMET 0.000 0.000 0.000 0.000 0.000
LAMBDA
TIMET
________
Y 0.000
TIMET 1.000
THETA
Y TIMET
________ ________
Y 0.000
TIMET 0.000 0.000
ALPHA
SY%2a S%2a SX%2a LOGV%2a Y
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
ALPHA
TIMET
________
0.000
BETA
SY%2a S%2a SX%2a LOGV%2a Y
________ ________ ________ ________ ________
SY%2a 0.000 0.000 0.000 0.000 0.000
S%2a 0.000 0.000 0.000 0.000 0.000
SX%2a 0.000 0.000 0.000 0.000 0.000
LOGV%2a 0.000 0.000 0.000 0.000 0.000
Y 0.000 0.000 0.000 0.000 0.000
TIMET 0.000 0.000 0.000 0.000 0.000
BETA
TIMET
________
SY%2a 0.000
S%2a 0.000
SX%2a 0.000
LOGV%2a 0.000
Y 0.000
TIMET 0.000
PSI
SY%2a S%2a SX%2a LOGV%2a Y
________ ________ ________ ________ ________
SY%2a 1.000
S%2a 0.000 0.000
SX%2a 0.000 0.000 1.000
LOGV%2a 0.000 0.000 0.000 0.000
Y 0.000 0.000 0.000 0.000 1.832
TIMET 0.000 0.000 0.000 0.000 0.000
PSI
TIMET
________
TIMET 416.625
STARTING VALUES FOR BETWEEN SUBJECT
NU
Y W XM
________ ________ ________
0.000 0.000 0.000
LAMBDA
SY%2b S%2b SX%2b LOGV%2b Y
________ ________ ________ ________ ________
Y 0.000 0.000 0.000 0.000 1.000
W 0.000 0.000 0.000 0.000 0.000
XM 0.000 0.000 0.000 0.000 0.000
LAMBDA
W XM
________ ________
Y 0.000 0.000
W 1.000 0.000
XM 0.000 1.000
THETA
Y W XM
________ ________ ________
Y 0.000
W 0.000 0.000
XM 0.000 0.000 0.000
ALPHA
SY%2b S%2b SX%2b LOGV%2b Y
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 1.999
ALPHA
W XM
________ ________
0.000 0.000
BETA
SY%2b S%2b SX%2b LOGV%2b Y
________ ________ ________ ________ ________
SY%2b 0.000 0.000 0.000 0.000 0.000
S%2b 0.000 0.000 0.000 0.000 0.000
SX%2b 0.000 0.000 0.000 0.000 0.000
LOGV%2b 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
W XM
________ ________
SY%2b 0.000 0.000
S%2b 0.000 0.000
SX%2b 0.000 0.000
LOGV%2b 0.000 0.000
Y 0.000 0.000
W 0.000 0.000
XM 0.000 0.000
PSI
SY%2b S%2b SX%2b LOGV%2b Y
________ ________ ________ ________ ________
SY%2b 1.000
S%2b 0.000 1.000
SX%2b 0.000 0.000 1.000
LOGV%2b 0.000 0.000 0.000 1.000
Y 0.000 0.000 0.000 0.000 1.832
W 0.000 0.000 0.000 0.000 0.000
XM 0.000 0.000 0.000 0.000 0.000
PSI
W XM
________ ________
W 0.547
XM 0.000 0.566
PRIORS FOR ALL PARAMETERS PRIOR MEAN PRIOR VARIANCE PRIOR STD. DEV.
Parameter 1~N(0.000,infinity) 0.0000 infinity infinity
Parameter 2~IW(0.000,-4) infinity infinity infinity
Parameter 3~IW(0.000,-4) infinity infinity infinity
Parameter 4~IW(0.000,-4) infinity infinity infinity
Parameter 5~IW(0.000,-4) infinity infinity infinity
Parameter 6~IW(0.000,-4) infinity infinity infinity
Parameter 7~IW(0.000,-4) infinity 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~N(0.000,infinity) 0.0000 infinity infinity
Parameter 18~N(0.000,infinity) 0.0000 infinity infinity
Parameter 19~N(0.000,infinity) 0.0000 infinity infinity
Parameter 20~N(0.000,infinity) 0.0000 infinity infinity
Parameter 21~N(0.000,infinity) 0.0000 infinity infinity
Parameter 22~N(0.000,infinity) 0.0000 infinity infinity
Parameter 23~IW(0.000,-6) infinity infinity infinity
Parameter 24~IW(0.000,-6) infinity infinity infinity
Parameter 25~IW(0.000,-6) infinity infinity infinity
Parameter 26~IW(0.000,-6) infinity infinity infinity
Parameter 27~IW(0.000,-6) infinity infinity infinity
Parameter 28~IW(0.000,-6) infinity infinity infinity
Parameter 29~IW(0.000,-6) infinity infinity infinity
Parameter 30~IW(0.000,-6) infinity infinity infinity
Parameter 31~IW(0.000,-6) infinity infinity infinity
Parameter 32~IW(0.000,-6) infinity infinity infinity
Parameter 33~IW(0.000,-6) infinity infinity infinity
Parameter 34~IW(0.000,-6) infinity infinity infinity
Parameter 35~IW(0.000,-6) infinity infinity infinity
Parameter 36~IW(0.000,-6) infinity infinity infinity
Parameter 37~IW(0.000,-6) 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 2.333 10
200 1.672 19
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: 23:49:03
Ending Time: 23:52:33
Elapsed Time: 00:03:30
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