Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:42 PM
INPUT INSTRUCTIONS
TITLE: cross-classified time series analysis with a univariate first-order
autoregressive AR(1) model for a continuous dependent variable with a
covariate, random intercept, and random slope
DATA: FILE = ex9.38.dat;
VARIABLE: NAMES = w xm y x time subject;
CLUSTER = subject time;
WITHIN = x;
BETWEEN = (subject)w xm;
LAGGED = y(1);
DEFINE: CENTER x (GROUPMEAN subject);
ANALYSIS: TYPE = CROSSCLASSIFIED RANDOM;
ESTIMATOR = BAYES;
PROCESSORS = 2;
!BITERATIONS = (2000);
FBITERATIONS = 100;
MODEL: %WITHIN%
sx | y ON x;
sy | y ON y&1;
logv | y;
%BETWEEN subject%
y sx sy logv ON w xm;
y sx-logv WITH y sx-logv;
%BETWEEN time%
y sx-sy WITH y sx-sy;
OUTPUT: TECH1 TECH8;
PLOT: TYPE = PLOT3;
FACTORS = ALL;
INPUT READING TERMINATED NORMALLY
cross-classified time series analysis with a univariate first-order
autoregressive AR(1) model for a continuous dependent variable with a
covariate, random intercept, and random slope
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 20000
Number of dependent variables 1
Number of independent variables 4
Number of continuous latent variables 3
Observed dependent variables
Continuous
Y
Observed independent variables
W XM X Y&1
Continuous latent variables
SX SY LOGV
Variables with special functions
Cluster variables SUBJECT TIME
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
Specifications for Bayes Factor Score Estimation
Number of imputed data sets 50
Iteration intervals for thinning 1
Input data file(s)
ex9.38.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
SUMMARY OF MISSING DATA PATTERNS
Number of missing data patterns 2
MISSING DATA PATTERNS (x = not missing)
1 2
Y x x
X x x
Y&1 x
W x x
XM x x
MISSING DATA PATTERN FREQUENCIES
Pattern Frequency Pattern Frequency
1 19800 2 200
COVARIANCE COVERAGE OF DATA
Minimum covariance coverage value 0.100
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 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
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
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 28
Information Criteria
Deviance (DIC) 57894.824
Estimated Number of Parameters (pD) 845.827
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
Y WITH
SX -0.019 0.035 0.315 -0.076 0.052
SY 0.007 0.005 0.070 -0.002 0.017
SX WITH
SY -0.001 0.003 0.390 -0.007 0.005
Variances
Y 0.521 0.084 0.000 0.393 0.721 *
SX 0.196 0.028 0.000 0.149 0.255 *
SY 0.002 0.001 0.000 0.001 0.004 *
Between SUBJECT Level
SX ON
W 0.233 0.032 0.000 0.173 0.294 *
XM 0.273 0.034 0.000 0.205 0.343 *
SY ON
W 0.070 0.012 0.000 0.050 0.095 *
XM 0.034 0.012 0.005 0.011 0.061 *
LOGV ON
W 0.009 0.011 0.240 -0.013 0.029
XM -0.007 0.012 0.310 -0.031 0.014
Y ON
W 0.324 0.064 0.000 0.197 0.456 *
XM 0.408 0.064 0.000 0.289 0.528 *
Y WITH
SX -0.015 0.026 0.270 -0.069 0.033
SY -0.012 0.009 0.100 -0.030 0.005
LOGV 0.005 0.008 0.210 -0.006 0.023
SX WITH
SY 0.000 0.005 0.475 -0.008 0.011
LOGV -0.001 0.004 0.350 -0.010 0.006
SY WITH
LOGV -0.002 0.001 0.085 -0.004 0.001
Intercepts
Y 2.074 0.060 0.000 1.949 2.190 *
SX 0.561 0.066 0.000 0.432 0.679 *
SY 0.332 0.013 0.000 0.308 0.360 *
LOGV 0.013 0.011 0.075 -0.005 0.034
Residual Variances
Y 0.576 0.062 0.000 0.479 0.719 *
SX 0.203 0.022 0.000 0.169 0.252 *
SY 0.018 0.003 0.000 0.013 0.023 *
LOGV 0.004 0.001 0.000 0.002 0.007 *
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 TIME
NU
Y
________
0
LAMBDA
SX%2a SY%2a LOGV%2a Y
________ ________ ________ ________
Y 0 0 0 0
THETA
Y
________
Y 0
ALPHA
SX%2a SY%2a LOGV%2a Y
________ ________ ________ ________
0 0 0 0
BETA
SX%2a SY%2a LOGV%2a Y
________ ________ ________ ________
SX%2a 0 0 0 0
SY%2a 0 0 0 0
LOGV%2a 0 0 0 0
Y 0 0 0 0
PSI
SX%2a SY%2a LOGV%2a Y
________ ________ ________ ________
SX%2a 1
SY%2a 2 3
LOGV%2a 0 0 0
Y 4 5 0 6
PARAMETER SPECIFICATION FOR BETWEEN SUBJECT
NU
Y W XM
________ ________ ________
0 0 0
LAMBDA
SX%2b SY%2b LOGV%2b 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%2b SY%2b LOGV%2b Y W
________ ________ ________ ________ ________
7 8 9 10 0
ALPHA
XM
________
0
BETA
SX%2b SY%2b LOGV%2b Y W
________ ________ ________ ________ ________
SX%2b 0 0 0 0 11
SY%2b 0 0 0 0 13
LOGV%2b 0 0 0 0 15
Y 0 0 0 0 17
W 0 0 0 0 0
XM 0 0 0 0 0
BETA
XM
________
SX%2b 12
SY%2b 14
LOGV%2b 16
Y 18
W 0
XM 0
PSI
SX%2b SY%2b LOGV%2b Y W
________ ________ ________ ________ ________
SX%2b 19
SY%2b 20 21
LOGV%2b 22 23 24
Y 25 26 27 28
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 0.490
Y&1 0.000 0.000 1.836
STARTING VALUES FOR BETWEEN TIME
NU
Y
________
0.000
LAMBDA
SX%2a SY%2a LOGV%2a Y
________ ________ ________ ________
Y 0.000 0.000 0.000 1.000
THETA
Y
________
Y 0.000
ALPHA
SX%2a SY%2a LOGV%2a Y
________ ________ ________ ________
0.000 0.000 0.000 0.000
BETA
SX%2a SY%2a LOGV%2a Y
________ ________ ________ ________
SX%2a 0.000 0.000 0.000 0.000
SY%2a 0.000 0.000 0.000 0.000
LOGV%2a 0.000 0.000 0.000 0.000
Y 0.000 0.000 0.000 0.000
PSI
SX%2a SY%2a LOGV%2a Y
________ ________ ________ ________
SX%2a 1.000
SY%2a 0.000 1.000
LOGV%2a 0.000 0.000 0.000
Y 0.000 0.000 0.000 1.832
STARTING VALUES FOR BETWEEN SUBJECT
NU
Y W XM
________ ________ ________
0.000 0.000 0.000
LAMBDA
SX%2b SY%2b LOGV%2b 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%2b SY%2b LOGV%2b Y W
________ ________ ________ ________ ________
0.000 0.000 0.000 1.999 0.000
ALPHA
XM
________
0.000
BETA
SX%2b SY%2b LOGV%2b Y W
________ ________ ________ ________ ________
SX%2b 0.000 0.000 0.000 0.000 0.000
SY%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
XM
________
SX%2b 0.000
SY%2b 0.000
LOGV%2b 0.000
Y 0.000
W 0.000
XM 0.000
PSI
SX%2b SY%2b LOGV%2b Y W
________ ________ ________ ________ ________
SX%2b 1.000
SY%2b 0.000 1.000
LOGV%2b 0.000 0.000 1.000
Y 0.000 0.000 0.000 1.832
W 0.000 0.000 0.000 0.000 0.547
XM 0.000 0.000 0.000 0.000 0.000
PSI
XM
________
XM 0.566
PRIORS FOR ALL PARAMETERS PRIOR MEAN PRIOR VARIANCE PRIOR STD. DEV.
Parameter 1~IW(0.000,-4) infinity 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~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~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~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
Parameter 23~IW(0.000,-5) infinity infinity infinity
Parameter 24~IW(0.000,-5) infinity infinity infinity
Parameter 25~IW(0.000,-5) infinity infinity infinity
Parameter 26~IW(0.000,-5) infinity infinity infinity
Parameter 27~IW(0.000,-5) infinity infinity infinity
Parameter 28~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 1.373 7
200 2.114 7
SUMMARIES OF PLAUSIBLE VALUES (N = NUMBER OF OBSERVATIONS * NUMBER OF IMPUTATIONS)
SAMPLE STATISTICS
Means
SX%2a SY%2a LOGV%2a SX%2b SY%2b
________ ________ ________ ________ ________
0.054 -0.011 0.000 0.455 0.326
Means
LOGV%2b B2a_Y B2b_Y
________ ________ ________
0.022 -0.067 2.059
Covariances
SX%2a SY%2a LOGV%2a SX%2b SY%2b
________ ________ ________ ________ ________
SX%2a 0.180
SY%2a -0.001 0.002
LOGV%2a 0.000 0.000 0.000
SX%2b 0.000 0.000 0.000 0.412
SY%2b 0.000 0.000 0.000 0.045 0.027
LOGV%2b 0.000 0.000 0.000 0.001 0.000
B2a_Y -0.015 0.007 0.000 0.000 0.000
B2b_Y 0.000 0.000 0.000 0.300 0.052
Covariances
LOGV%2b B2a_Y B2b_Y
________ ________ ________
LOGV%2b 0.003
B2a_Y 0.000 0.482
B2b_Y -0.003 -0.001 0.999
Correlations
SX%2a SY%2a LOGV%2a SX%2b SY%2b
________ ________ ________ ________ ________
SX%2a 1.000
SY%2a -0.052 1.000
LOGV%2a 999.000 999.000 1.000
SX%2b -0.002 0.001 999.000 1.000
SY%2b 0.000 -0.002 999.000 0.431 1.000
LOGV%2b -0.006 0.002 999.000 0.029 0.042
B2a_Y -0.052 0.249 999.000 -0.001 0.000
B2b_Y -0.001 0.001 999.000 0.468 0.315
Correlations
LOGV%2b B2a_Y B2b_Y
________ ________ ________
LOGV%2b 1.000
B2a_Y -0.002 1.000
B2b_Y -0.055 -0.001 1.000
SUMMARY OF PLAUSIBLE STANDARD DEVIATION (N = NUMBER OF OBSERVATIONS)
SAMPLE STATISTICS
Means
SX%2a_SD SY%2a_SD LOGV%2a_ SX%2b_SD SY%2b_SD
________ ________ ________ ________ ________
0.077 0.033 0.000 0.103 0.065
Means
LOGV%2b_ B2a_Y_SD B2b_Y_SD
________ ________ ________
0.047 0.077 0.155
Covariances
SX%2a_SD SY%2a_SD LOGV%2a_ SX%2b_SD SY%2b_SD
________ ________ ________ ________ ________
SX%2a_SD 0.000
SY%2a_SD 0.000 0.000
LOGV%2a_ 0.000 0.000 0.000
SX%2b_SD 0.000 0.000 0.000 0.000
SY%2b_SD 0.000 0.000 0.000 0.000 0.000
LOGV%2b_ 0.000 0.000 0.000 0.000 0.000
B2a_Y_SD 0.000 0.000 0.000 0.000 0.000
B2b_Y_SD 0.000 0.000 0.000 0.000 0.000
Covariances
LOGV%2b_ B2a_Y_SD B2b_Y_SD
________ ________ ________
LOGV%2b_ 0.000
B2a_Y_SD 0.000 0.000
B2b_Y_SD 0.000 0.000 0.002
Correlations
SX%2a_SD SY%2a_SD LOGV%2a_ SX%2b_SD SY%2b_SD
________ ________ ________ ________ ________
SX%2a_SD 1.000
SY%2a_SD -0.065 1.000
LOGV%2a_ 999.000 999.000 1.000
SX%2b_SD 0.000 0.000 999.000 1.000
SY%2b_SD 0.000 0.000 999.000 0.019 1.000
LOGV%2b_ 0.000 0.000 999.000 -0.031 0.061
B2a_Y_SD 0.074 0.119 999.000 0.000 0.000
B2b_Y_SD 0.000 0.000 999.000 -0.118 -0.436
Correlations
LOGV%2b_ B2a_Y_SD B2b_Y_SD
________ ________ ________
LOGV%2b_ 1.000
B2a_Y_SD 0.000 1.000
B2b_Y_SD 0.161 0.000 1.000
PLOT INFORMATION
The following plots are available:
Histograms (sample values, estimated factor scores)
Scatterplots (sample values, estimated factor scores)
Between-level histograms (sample values, sample means/variances, estimated factor scores)
Between-level scatterplots (sample values, sample means/variances, estimated factor scores)
Time series plots (sample values, ACF, PACF, estimated factor scores)
Histogram of subjects per time point
Bayesian posterior parameter distributions
Bayesian posterior parameter trace plots
Bayesian autocorrelation plots
Latent variable distribution plots
Beginning Time: 23:42:16
Ending Time: 23:47:16
Elapsed Time: 00:05:00
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