Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:36 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a two-level time series analysis
with a first-order autoregressive AR(1) confirmatory factor analysis (CFA) model
for continuous factor indicators with random intercepts, a random AR(1) slope,
and a random residual variance
DATA: FILE = ex9.34.dat;
VARIABLE: NAMES = y1-y4 subject;
CLUSTER = subject;
ANALYSIS: TYPE = TWOLEVEL RANDOM;
ESTIMATOR = BAYES;
PROCESSORS = 2;
BITERATIONS = (2000);
MODEL: %WITHIN%
f BY y1-y4(&1);
s | f ON f&1;
logv | f;
%BETWEEN%
fb BY y1-y4*;
fb@1;
fb s logv WITH fb s logv;
OUTPUT: TECH1 TECH8;
PLOT: TYPE = PLOT3;
INPUT READING TERMINATED NORMALLY
this is an example of a two-level time series analysis
with a first-order autoregressive AR(1) confirmatory factor analysis (CFA) model
for continuous factor indicators with random intercepts, a random AR(1) slope,
and a random residual variance
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 20000
Number of dependent variables 4
Number of independent variables 0
Number of continuous latent variables 5
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4
Continuous latent variables
F F&1 FB S LOGV
Variables with special functions
Cluster variable SUBJECT
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)
ex9.34.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
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
Y1 0.074 0.031 -6.095 0.01% -1.194 -0.312 0.060
20000.000 2.272 -0.023 5.966 0.01% 0.438 1.343
Y2 0.029 -0.030 -6.340 0.01% -1.261 -0.353 0.041
20000.000 2.346 -0.017 6.551 0.01% 0.430 1.335
Y3 0.014 0.009 -6.011 0.01% -1.266 -0.373 0.019
20000.000 2.345 -0.037 6.411 0.01% 0.408 1.298
Y4 -0.049 0.016 -6.845 0.01% -1.321 -0.441 -0.054
20000.000 2.296 0.018 6.087 0.01% 0.329 1.228
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 26
Information Criteria
Deviance (DIC) 189996.355
Estimated Number of Parameters (pD) 18216.929
MODEL RESULTS
Posterior One-Tailed 95% C.I.
Estimate S.D. P-Value Lower 2.5% Upper 2.5% Significance
Within Level
F BY
Y1 1.000 0.000 0.000 1.000 1.000
Y2 1.001 0.007 0.000 0.987 1.015 *
Y3 0.999 0.007 0.000 0.985 1.012 *
Y4 0.994 0.007 0.000 0.980 1.009 *
Residual Variances
Y1 0.495 0.007 0.000 0.482 0.508 *
Y2 0.500 0.007 0.000 0.487 0.514 *
Y3 0.499 0.007 0.000 0.486 0.512 *
Y4 0.511 0.007 0.000 0.496 0.524 *
Between Level
FB BY
Y1 0.600 0.055 0.000 0.490 0.709 *
Y2 0.661 0.058 0.000 0.556 0.778 *
Y3 0.653 0.057 0.000 0.549 0.774 *
Y4 0.606 0.058 0.000 0.498 0.729 *
FB WITH
S 0.012 0.015 0.193 -0.016 0.042
LOGV -0.014 0.015 0.162 -0.044 0.013
S WITH
LOGV -0.004 0.002 0.026 -0.009 0.000
Means
S 0.300 0.012 0.000 0.277 0.322 *
LOGV 0.003 0.016 0.424 -0.027 0.035
Intercepts
Y1 0.074 0.060 0.095 -0.037 0.200
Y2 0.030 0.062 0.309 -0.091 0.152
Y3 0.013 0.063 0.416 -0.105 0.139
Y4 -0.046 0.060 0.218 -0.166 0.071
Variances
FB 1.000 0.000 0.000 1.000 1.000
S 0.019 0.003 0.000 0.014 0.026 *
LOGV 0.012 0.003 0.000 0.006 0.019 *
Residual Variances
Y1 0.300 0.041 0.000 0.230 0.385 *
Y2 0.290 0.042 0.000 0.217 0.378 *
Y3 0.305 0.043 0.000 0.228 0.397 *
Y4 0.319 0.042 0.000 0.247 0.413 *
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
NU
Y1 Y2 Y3 Y4
________ ________ ________ ________
0 0 0 0
LAMBDA
F F&1
________ ________
Y1 0 0
Y2 1 0
Y3 2 0
Y4 3 0
THETA
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 4
Y2 0 5
Y3 0 0 6
Y4 0 0 0 7
ALPHA
F F&1
________ ________
0 0
BETA
F F&1
________ ________
F 0 0
F&1 0 0
PSI
F F&1
________ ________
F 0
F&1 0 0
PARAMETER SPECIFICATION FOR BETWEEN
NU
Y1 Y2 Y3 Y4
________ ________ ________ ________
8 9 10 11
LAMBDA
FB S LOGV
________ ________ ________
Y1 12 0 0
Y2 13 0 0
Y3 14 0 0
Y4 15 0 0
THETA
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 16
Y2 0 17
Y3 0 0 18
Y4 0 0 0 19
ALPHA
FB S LOGV
________ ________ ________
0 20 21
BETA
FB S LOGV
________ ________ ________
FB 0 0 0
S 0 0 0
LOGV 0 0 0
PSI
FB S LOGV
________ ________ ________
FB 0
S 22 23
LOGV 24 25 26
STARTING VALUES FOR WITHIN
NU
Y1 Y2 Y3 Y4
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
F F&1
________ ________
Y1 1.000 0.000
Y2 1.000 0.000
Y3 1.000 0.000
Y4 1.000 0.000
THETA
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 1.136
Y2 0.000 1.173
Y3 0.000 0.000 1.172
Y4 0.000 0.000 0.000 1.148
ALPHA
F F&1
________ ________
0.000 0.000
BETA
F F&1
________ ________
F 0.000 0.000
F&1 0.000 0.000
PSI
F F&1
________ ________
F 0.000
F&1 0.000 1.000
STARTING VALUES FOR BETWEEN
NU
Y1 Y2 Y3 Y4
________ ________ ________ ________
0.074 0.029 0.014 -0.049
LAMBDA
FB S LOGV
________ ________ ________
Y1 1.000 0.000 0.000
Y2 1.000 0.000 0.000
Y3 1.000 0.000 0.000
Y4 1.000 0.000 0.000
THETA
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 1.136
Y2 0.000 1.173
Y3 0.000 0.000 1.172
Y4 0.000 0.000 0.000 1.148
ALPHA
FB S LOGV
________ ________ ________
0.000 0.000 0.000
BETA
FB S LOGV
________ ________ ________
FB 0.000 0.000 0.000
S 0.000 0.000 0.000
LOGV 0.000 0.000 0.000
PSI
FB S LOGV
________ ________ ________
FB 1.000
S 0.000 1.000
LOGV 0.000 0.000 1.000
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~IG(-1.000,0.000) infinity infinity infinity
Parameter 5~IG(-1.000,0.000) infinity infinity infinity
Parameter 6~IG(-1.000,0.000) infinity infinity infinity
Parameter 7~IG(-1.000,0.000) 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~IG(-1.000,0.000) infinity infinity infinity
Parameter 17~IG(-1.000,0.000) infinity infinity infinity
Parameter 18~IG(-1.000,0.000) infinity infinity infinity
Parameter 19~IG(-1.000,0.000) infinity infinity infinity
Parameter 20~N(0.000,infinity) 0.0000 infinity infinity
Parameter 21~N(0.000,infinity) 0.0000 infinity infinity
Parameter 22~IW(0.000,-4)
Parameter 23~IW(0.000,-4)
Parameter 24~IW(0.000,-4)
Parameter 25~IW(0.000,-4)
Parameter 26~IW(0.000,-4)
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION
CHAIN BSEED
1 0
2 285380
POTENTIAL PARAMETER WITH
ITERATION SCALE REDUCTION HIGHEST PSR
100 1.229 9
200 1.711 21
300 1.117 21
400 1.253 21
500 1.077 21
600 1.026 26
700 1.034 26
800 1.051 26
900 1.137 21
1000 1.091 21
1100 1.042 21
1200 1.011 13
1300 1.032 22
1400 1.031 22
1500 1.037 22
1600 1.041 22
1700 1.041 24
1800 1.032 24
1900 1.024 24
2000 1.040 21
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: 23:36:04
Ending Time: 23:36:34
Elapsed Time: 00:00:30
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