Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:38 PM
INPUT INSTRUCTIONS
TITLE: two-level time series analysis with a univariate first-order autoregressive AR(1) m
for a continuous dependent variable with a covariate, linear trend, random slopes,
and a random residual variance
DATA: FILE = ex9.37.dat;
VARIABLE: NAMES = y x w xm time subject;
WITHIN = x time;
BETWEEN = w xm;
CLUSTER = subject;
LAGGED = y(1);
DEFINE: CENTER x (GROUPMEAN);
ANALYSIS: TYPE = TWOLEVEL RANDOM;
ESTIMATOR = BAYES;
PROCESSORS = 2;
BITERATIONS = (3000);
MODEL: %WITHIN%
sy | y ON y&1;
sx | y ON x;
s | y ON time;
logv | y;
%BETWEEN%
sy ON w xm;
sx ON w xm;
s ON w xm;
logv ON w xm;
y ON w xm;
sy-logv y WITH sy-logv y;
OUTPUT: TECH1 TECH8;
PLOT: TYPE= PLOT3;
*** WARNING
Input line exceeded 90 characters. Some input may be truncated.
TITLE: two-level time series analysis with a univariate first-order autoregressive AR(1) mo
1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
two-level time series analysis with a univariate first-order autoregressive AR(1) mo
for a continuous dependent variable with a covariate, linear trend, random slopes,
and a random residual variance
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 20000
Number of dependent variables 1
Number of independent variables 5
Number of continuous latent variables 4
Observed dependent variables
Continuous
Y
Observed independent variables
X W XM TIME Y&1
Continuous latent variables
SY SX S LOGV
Variables with special functions
Cluster variable SUBJECT
Within variables
X TIME 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)
ex9.37.dat
Input data format FREE
SUMMARY OF DATA
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 TIME W XM
________ ________ ________ ________ ________
Y 1.000
X 1.000 1.000
TIME 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
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 1.950 0.271 -4.681 0.01% 0.512 1.469 1.876
20000.000 2.956 0.425 11.083 0.01% 2.314 3.344
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
TIME 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
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 30
Information Criteria
Deviance (DIC) 57879.089
Estimated Number of Parameters (pD) 773.982
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 0.078 0.013 0.000 0.052 0.102 *
XM 0.031 0.012 0.005 0.007 0.055 *
SX ON
W 0.234 0.036 0.000 0.168 0.306 *
XM 0.273 0.035 0.000 0.200 0.339 *
S ON
W 0.000 0.000 0.188 -0.001 0.000
XM 0.000 0.000 0.298 -0.001 0.001
LOGV ON
W 0.008 0.011 0.224 -0.013 0.031
XM -0.001 0.011 0.464 -0.023 0.021
Y ON
W 0.358 0.069 0.000 0.221 0.490 *
XM 0.399 0.066 0.000 0.271 0.532 *
SY WITH
SX 0.001 0.006 0.411 -0.010 0.012
S 0.000 0.000 0.343 0.000 0.000
LOGV -0.001 0.002 0.263 -0.005 0.002
Y -0.015 0.010 0.072 -0.036 0.005
SX WITH
S 0.000 0.000 0.322 0.000 0.000
LOGV -0.003 0.006 0.316 -0.014 0.008
Y -0.003 0.029 0.451 -0.060 0.057
S WITH
LOGV 0.000 0.000 0.496 0.000 0.000
Y -0.001 0.000 0.001 -0.002 0.000 *
LOGV WITH
Y 0.008 0.010 0.220 -0.012 0.029
Intercepts
Y 1.992 0.060 0.000 1.874 2.110 *
SY 0.316 0.011 0.000 0.294 0.339 *
SX 0.522 0.033 0.000 0.454 0.582 *
S 0.000 0.000 0.443 -0.001 0.001
LOGV 0.018 0.011 0.058 -0.008 0.037
Residual Variances
Y 0.612 0.077 0.000 0.483 0.778 *
SY 0.019 0.003 0.000 0.014 0.024 *
SX 0.208 0.023 0.000 0.170 0.259 *
S 0.000 0.000 0.000 0.000 0.000 *
LOGV 0.004 0.002 0.000 0.002 0.008 *
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
NU
Y X TIME Y&1
________ ________ ________ ________
0 0 0 0
LAMBDA
Y X TIME Y&1
________ ________ ________ ________
Y 0 0 0 0
X 0 0 0 0
TIME 0 0 0 0
Y&1 0 0 0 0
THETA
Y X TIME Y&1
________ ________ ________ ________
Y 0
X 0 0
TIME 0 0 0
Y&1 0 0 0 0
ALPHA
Y X TIME Y&1
________ ________ ________ ________
0 0 0 0
BETA
Y X TIME Y&1
________ ________ ________ ________
Y 0 0 0 0
X 0 0 0 0
TIME 0 0 0 0
Y&1 0 0 0 0
PSI
Y X TIME Y&1
________ ________ ________ ________
Y 0
X 0 0
TIME 0 0 0
Y&1 0 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN
NU
Y W XM
________ ________ ________
0 0 0
LAMBDA
SY SX S LOGV 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 SX S LOGV Y
________ ________ ________ ________ ________
1 2 3 4 5
ALPHA
W XM
________ ________
0 0
BETA
SY SX S LOGV Y
________ ________ ________ ________ ________
SY 0 0 0 0 0
SX 0 0 0 0 0
S 0 0 0 0 0
LOGV 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 6 7
SX 8 9
S 10 11
LOGV 12 13
Y 14 15
W 0 0
XM 0 0
PSI
SY SX S LOGV Y
________ ________ ________ ________ ________
SY 16
SX 17 18
S 19 20 21
LOGV 22 23 24 25
Y 26 27 28 29 30
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 TIME Y&1
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
Y X TIME Y&1
________ ________ ________ ________
Y 1.000 0.000 0.000 0.000
X 0.000 1.000 0.000 0.000
TIME 0.000 0.000 1.000 0.000
Y&1 0.000 0.000 0.000 1.000
THETA
Y X TIME Y&1
________ ________ ________ ________
Y 0.000
X 0.000 0.000
TIME 0.000 0.000 0.000
Y&1 0.000 0.000 0.000 0.000
ALPHA
Y X TIME Y&1
________ ________ ________ ________
0.000 0.000 0.000 0.000
BETA
Y X TIME Y&1
________ ________ ________ ________
Y 0.000 0.000 0.000 0.000
X 0.000 0.000 0.000 0.000
TIME 0.000 0.000 0.000 0.000
Y&1 0.000 0.000 0.000 0.000
PSI
Y X TIME Y&1
________ ________ ________ ________
Y 0.000
X 0.000 0.490
TIME 0.000 0.000 416.625
Y&1 0.000 0.000 0.000 1.479
STARTING VALUES FOR BETWEEN
NU
Y W XM
________ ________ ________
0.000 0.000 0.000
LAMBDA
SY SX S LOGV 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 SX S LOGV Y
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 1.950
ALPHA
W XM
________ ________
0.000 0.000
BETA
SY SX S LOGV Y
________ ________ ________ ________ ________
SY 0.000 0.000 0.000 0.000 0.000
SX 0.000 0.000 0.000 0.000 0.000
S 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
W XM
________ ________
SY 0.000 0.000
SX 0.000 0.000
S 0.000 0.000
LOGV 0.000 0.000
Y 0.000 0.000
W 0.000 0.000
XM 0.000 0.000
PSI
SY SX S LOGV Y
________ ________ ________ ________ ________
SY 1.000
SX 0.000 1.000
S 0.000 0.000 1.000
LOGV 0.000 0.000 0.000 1.000
Y 0.000 0.000 0.000 0.000 1.478
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~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~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,-6) infinity infinity infinity
Parameter 17~IW(0.000,-6) infinity infinity infinity
Parameter 18~IW(0.000,-6) infinity infinity infinity
Parameter 19~IW(0.000,-6) infinity infinity infinity
Parameter 20~IW(0.000,-6) infinity infinity infinity
Parameter 21~IW(0.000,-6) infinity infinity infinity
Parameter 22~IW(0.000,-6) infinity 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
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION
CHAIN BSEED
1 0
2 285380
POTENTIAL PARAMETER WITH
ITERATION SCALE REDUCTION HIGHEST PSR
100 1.210 13
200 1.313 4
300 1.198 23
400 1.099 13
500 1.258 29
600 1.271 29
700 1.241 29
800 1.301 13
900 1.265 13
1000 1.214 13
1100 1.128 13
1200 1.154 13
1300 1.081 13
1400 1.064 13
1500 1.057 13
1600 1.054 4
1700 1.042 4
1800 1.066 4
1900 1.033 4
2000 1.055 4
2100 1.048 13
2200 1.044 13
2300 1.065 13
2400 1.047 13
2500 1.036 13
2600 1.026 23
2700 1.019 23
2800 1.022 23
2900 1.026 12
3000 1.018 23
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: 23:38:25
Ending Time: 23:39:15
Elapsed Time: 00:00:50
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