Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:47 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;
CENTER x (GROUPMEAN subject);
ANALYSIS: TYPE = CROSSCLASSIFIED RANDOM;
ESTIMATOR = BAYES;
PROCESSORS = 2;
BITERATIONS = (5000);
MODEL: %WITHIN%
y ON y&1;
s | y ON timew;
sx | y ON x;
%BETWEEN subject%
y s sx ON w xm;
y s sx WITH y s sx;
%BETWEEN time%
sx ON timet;
y WITH 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 2
Observed dependent variables
Continuous
Y
Observed independent variables
W XM X TIMEW TIMET Y&1
Continuous latent variables
S SX
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)
Convergence criterion 0.500D-01
Maximum number of iterations 50000
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 0.000 0.027 -3.876 0.01% -0.834 -0.258 -0.002
20000.000 0.981 -0.015 3.891 0.01% 0.245 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 21
Information Criteria
Deviance (DIC) 58984.565
Estimated Number of Parameters (pD) 653.699
MODEL RESULTS
Posterior One-Tailed 95% C.I.
Estimate S.D. P-Value Lower 2.5% Upper 2.5% Significance
Within Level
Y ON
Y&1 0.363 0.005 0.000 0.353 0.373 *
Residual Variances
Y 1.082 0.011 0.000 1.061 1.103 *
Between TIME Level
SX ON
TIMET -0.002 0.002 0.054 -0.007 0.000
Y WITH
SX -0.018 0.037 0.311 -0.094 0.055
Variances
Y 0.534 0.084 0.000 0.401 0.729 *
S 0.000 0.000 0.000 0.000 0.000
Residual Variances
SX 0.213 0.039 0.000 0.155 0.306 *
Between SUBJECT Level
S ON
W 0.000 0.000 0.095 -0.001 0.000
XM 0.000 0.000 0.123 -0.001 0.000
SX ON
W 0.221 0.037 0.000 0.149 0.294 *
XM 0.253 0.036 0.000 0.182 0.323 *
Y ON
W 0.337 0.064 0.000 0.213 0.463 *
XM 0.419 0.064 0.000 0.295 0.546 *
Y WITH
S 0.000 0.000 0.026 -0.001 0.000
SX 0.000 0.029 0.498 -0.058 0.057
S WITH
SX 0.000 0.000 0.097 0.000 0.000
Intercepts
Y 1.989 0.129 0.000 1.723 2.239 *
S 0.002 0.001 0.055 0.000 0.004
SX 0.727 0.119 0.000 0.550 1.014 *
Residual Variances
Y 0.613 0.073 0.000 0.488 0.772 *
S 0.000 0.000 0.000 0.000 0.000 *
SX 0.205 0.023 0.000 0.167 0.255 *
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 1
X 0 0 0 0
TIMEW 0 0 0 0
Y&1 0 0 0 0
PSI
Y X TIMEW Y&1
________ ________ ________ ________
Y 2
X 0 0
TIMEW 0 0 0
Y&1 0 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN TIME
NU
Y TIMET
________ ________
0 0
LAMBDA
S%2a SX%2a Y TIMET
________ ________ ________ ________
Y 0 0 0 0
TIMET 0 0 0 0
THETA
Y TIMET
________ ________
Y 0
TIMET 0 0
ALPHA
S%2a SX%2a Y TIMET
________ ________ ________ ________
0 0 0 0
BETA
S%2a SX%2a Y TIMET
________ ________ ________ ________
S%2a 0 0 0 0
SX%2a 0 0 0 3
Y 0 0 0 0
TIMET 0 0 0 0
PSI
S%2a SX%2a Y TIMET
________ ________ ________ ________
S%2a 0
SX%2a 0 4
Y 0 5 6
TIMET 0 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN SUBJECT
NU
Y W XM
________ ________ ________
0 0 0
LAMBDA
S%2b SX%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
S%2b SX%2b Y W XM
________ ________ ________ ________ ________
7 8 9 0 0
BETA
S%2b SX%2b Y W XM
________ ________ ________ ________ ________
S%2b 0 0 0 10 11
SX%2b 0 0 0 12 13
Y 0 0 0 14 15
W 0 0 0 0 0
XM 0 0 0 0 0
PSI
S%2b SX%2b Y W XM
________ ________ ________ ________ ________
S%2b 16
SX%2b 17 18
Y 19 20 21
W 0 0 0 0
XM 0 0 0 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 1.832
X 0.000 0.490
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
S%2a SX%2a Y TIMET
________ ________ ________ ________
Y 0.000 0.000 1.000 0.000
TIMET 0.000 0.000 0.000 1.000
THETA
Y TIMET
________ ________
Y 0.000
TIMET 0.000 0.000
ALPHA
S%2a SX%2a Y TIMET
________ ________ ________ ________
0.000 0.000 0.000 0.000
BETA
S%2a SX%2a Y TIMET
________ ________ ________ ________
S%2a 0.000 0.000 0.000 0.000
SX%2a 0.000 0.000 0.000 0.000
Y 0.000 0.000 0.000 0.000
TIMET 0.000 0.000 0.000 0.000
PSI
S%2a SX%2a Y TIMET
________ ________ ________ ________
S%2a 0.000
SX%2a 0.000 1.000
Y 0.000 0.000 1.832
TIMET 0.000 0.000 0.000 416.625
STARTING VALUES FOR BETWEEN SUBJECT
NU
Y W XM
________ ________ ________
0.000 0.000 0.000
LAMBDA
S%2b SX%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
S%2b SX%2b Y W XM
________ ________ ________ ________ ________
0.000 0.000 1.999 0.000 0.000
BETA
S%2b SX%2b Y W XM
________ ________ ________ ________ ________
S%2b 0.000 0.000 0.000 0.000 0.000
SX%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
PSI
S%2b SX%2b Y W XM
________ ________ ________ ________ ________
S%2b 1.000
SX%2b 0.000 1.000
Y 0.000 0.000 1.832
W 0.000 0.000 0.000 0.547
XM 0.000 0.000 0.000 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~IG(-1.000,0.000) infinity infinity infinity
Parameter 3~N(0.000,infinity) 0.0000 infinity infinity
Parameter 4~IW(0.000,-3) infinity infinity infinity
Parameter 5~IW(0.000,-3) infinity infinity infinity
Parameter 6~IW(0.000,-3) infinity 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~IW(0.000,-4) infinity infinity infinity
Parameter 17~IW(0.000,-4) infinity infinity infinity
Parameter 18~IW(0.000,-4) infinity infinity infinity
Parameter 19~IW(0.000,-4) infinity infinity infinity
Parameter 20~IW(0.000,-4) infinity infinity infinity
Parameter 21~IW(0.000,-4) 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 4.050 8
200 1.451 8
300 1.172 9
400 2.075 9
500 3.104 9
600 2.403 9
700 1.790 9
800 1.730 8
900 1.792 8
1000 1.573 8
1100 1.323 8
1200 1.416 9
1300 1.655 9
1400 1.824 9
1500 2.141 9
1600 2.071 9
1700 2.069 9
1800 2.072 9
1900 1.997 9
2000 2.005 9
2100 1.883 9
2200 1.835 9
2300 1.508 9
2400 1.369 9
2500 1.326 9
2600 1.294 9
2700 1.277 9
2800 1.220 9
2900 1.222 8
3000 1.298 8
3100 1.338 8
3200 1.327 8
3300 1.381 8
3400 1.472 8
3500 1.529 8
3600 1.566 8
3700 1.584 8
3800 1.572 8
3900 1.494 8
4000 1.467 8
4100 1.409 8
4200 1.305 8
4300 1.208 9
4400 1.223 9
4500 1.233 9
4600 1.265 9
4700 1.279 9
4800 1.277 9
4900 1.258 9
5000 1.235 9
5100 1.243 9
5200 1.224 9
5300 1.207 9
5400 1.186 9
5500 1.191 9
5600 1.183 9
5700 1.188 9
5800 1.195 9
5900 1.192 9
6000 1.183 9
6100 1.170 9
6200 1.172 9
6300 1.155 9
6400 1.135 9
6500 1.121 9
6600 1.096 9
6700 1.074 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: 23:47:16
Ending Time: 23:49:03
Elapsed Time: 00:01:47
MUTHEN & MUTHEN
3463 Stoner Ave.
Los Angeles, CA 90066
Tel: (310) 391-9971
Fax: (310) 391-8971
Web: www.StatModel.com
Support: Support@StatModel.com
Copyright (c) 1998-2022 Muthen & Muthen