Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:37 PM
INPUT INSTRUCTIONS
TITLE: two-level time series analysis with a bivariate cross-lagged model
for two factors and continuous factor indicators with random intercepts
and random slopes
DATA: FILE = ex9.36.dat;
VARIABLE: NAMES = y11-y14 y21-y24 subject;
CLUSTER = subject;
ANALYSIS: TYPE = TWOLEVEL RANDOM;
ESTIMATOR = BAYES;
PROCESSORS = 2;
BITERATIONS = (2000);
MODEL: %WITHIN%
f1 BY y11-y14(&1);
f2 BY y21-y24(&1);
s11 | f1 ON f1&1;
s22 | f2 ON f2&1;
s12 | f1 ON f2&1;
s21 | f2 ON f1&1;
%BETWEEN%
fb1 BY y11-y14*;
fb2 BY y21-y24*;
fb1-fb2@1;
fb1 fb2 s11-s21 WITH fb1 fb2 s11-s21;
OUTPUT: TECH1 TECH8;
PLOT: TYPE = PLOT3;
INPUT READING TERMINATED NORMALLY
two-level time series analysis with a bivariate cross-lagged model
for two factors and continuous factor indicators with random intercepts
and random slopes
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 20000
Number of dependent variables 8
Number of independent variables 0
Number of continuous latent variables 10
Observed dependent variables
Continuous
Y11 Y12 Y13 Y14 Y21 Y22
Y23 Y24
Continuous latent variables
F1 F2 F1&1 F2&1 FB1 FB2
S11 S22 S12 S21
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)
ex9.36.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
Y11 -0.046 -0.006 -5.661 0.01% -1.248 -0.410 -0.033
20000.000 2.084 -0.007 5.222 0.01% 0.321 1.166
Y12 -0.113 -0.036 -6.682 0.01% -1.334 -0.474 -0.104
20000.000 2.099 0.044 5.400 0.01% 0.273 1.104
Y13 -0.039 0.013 -5.326 0.01% -1.225 -0.398 -0.043
20000.000 2.006 0.038 5.108 0.01% 0.312 1.151
Y14 -0.088 -0.007 -5.746 0.01% -1.301 -0.463 -0.093
20000.000 2.095 -0.012 5.800 0.01% 0.275 1.140
Y21 -0.032 -0.007 -5.808 0.01% -1.309 -0.397 -0.014
20000.000 2.285 0.086 5.926 0.01% 0.357 1.229
Y22 0.016 0.016 -5.704 0.01% -1.254 -0.363 0.024
20000.000 2.291 0.058 6.217 0.01% 0.389 1.271
Y23 0.009 0.017 -5.901 0.01% -1.278 -0.370 0.007
20000.000 2.326 0.021 6.070 0.01% 0.382 1.284
Y24 -0.034 -0.014 -6.739 0.01% -1.271 -0.404 -0.032
20000.000 2.212 0.128 5.903 0.01% 0.338 1.209
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 64
Information Criteria
Deviance (DIC) 380425.675
Estimated Number of Parameters (pD) 36126.395
MODEL RESULTS
Posterior One-Tailed 95% C.I.
Estimate S.D. P-Value Lower 2.5% Upper 2.5% Significance
Within Level
F1 BY
Y11 1.000 0.000 0.000 1.000 1.000
Y12 0.991 0.008 0.000 0.976 1.006 *
Y13 1.009 0.008 0.000 0.994 1.024 *
Y14 0.998 0.008 0.000 0.984 1.013 *
F2 BY
Y21 1.000 0.000 0.000 1.000 1.000
Y22 1.007 0.007 0.000 0.993 1.021 *
Y23 1.007 0.007 0.000 0.993 1.020 *
Y24 1.001 0.007 0.000 0.988 1.015 *
F2 WITH
F1 0.259 0.009 0.000 0.243 0.276 *
Residual Variances
Y11 0.510 0.007 0.000 0.496 0.524 *
Y12 0.504 0.007 0.000 0.491 0.517 *
Y13 0.492 0.007 0.000 0.479 0.506 *
Y14 0.512 0.007 0.000 0.498 0.525 *
Y21 0.497 0.007 0.000 0.484 0.510 *
Y22 0.506 0.007 0.000 0.493 0.519 *
Y23 0.504 0.007 0.000 0.491 0.517 *
Y24 0.506 0.007 0.000 0.493 0.520 *
F1 1.009 0.015 0.000 0.980 1.039 *
F2 0.996 0.014 0.000 0.968 1.023 *
Between Level
FB1 BY
Y11 0.526 0.047 0.000 0.437 0.621 *
Y12 0.546 0.049 0.000 0.453 0.645 *
Y13 0.447 0.044 0.000 0.366 0.537 *
Y14 0.533 0.047 0.000 0.441 0.626 *
FB2 BY
Y21 0.534 0.049 0.000 0.441 0.639 *
Y22 0.515 0.049 0.000 0.420 0.619 *
Y23 0.600 0.047 0.000 0.513 0.701 *
Y24 0.518 0.043 0.000 0.439 0.605 *
FB1 WITH
FB2 0.561 0.068 0.000 0.418 0.681 *
S11 0.014 0.015 0.178 -0.016 0.046
S22 0.006 0.015 0.341 -0.024 0.035
S12 -0.022 0.015 0.065 -0.053 0.007
S21 0.003 0.016 0.409 -0.028 0.034
FB2 WITH
S11 -0.006 0.015 0.353 -0.036 0.024
S22 -0.012 0.016 0.224 -0.044 0.019
S12 -0.020 0.016 0.097 -0.051 0.011
S21 0.010 0.016 0.271 -0.022 0.040
S11 WITH
S22 0.001 0.003 0.342 -0.004 0.006
S12 0.002 0.003 0.168 -0.002 0.007
S21 0.002 0.002 0.235 -0.003 0.007
S22 WITH
S12 0.002 0.002 0.168 -0.003 0.007
S21 0.002 0.003 0.219 -0.003 0.007
S12 WITH
S21 0.001 0.002 0.276 -0.003 0.006
Means
S11 0.183 0.013 0.000 0.158 0.209 *
S22 0.306 0.013 0.000 0.279 0.331 *
S12 0.084 0.013 0.000 0.058 0.110 *
S21 0.207 0.014 0.000 0.180 0.235 *
Intercepts
Y11 -0.048 0.049 0.169 -0.140 0.050
Y12 -0.113 0.050 0.010 -0.210 -0.017 *
Y13 -0.042 0.045 0.185 -0.128 0.047
Y14 -0.092 0.049 0.035 -0.189 0.004
Y21 -0.031 0.054 0.267 -0.136 0.077
Y22 0.018 0.053 0.373 -0.082 0.124
Y23 0.012 0.055 0.419 -0.097 0.121
Y24 -0.035 0.050 0.249 -0.131 0.063
Variances
FB1 1.000 0.000 0.000 1.000 1.000
FB2 1.000 0.000 0.000 1.000 1.000
S11 0.020 0.003 0.000 0.014 0.028 *
S22 0.023 0.003 0.000 0.017 0.030 *
S12 0.023 0.004 0.000 0.017 0.031 *
S21 0.022 0.004 0.000 0.015 0.031 *
Residual Variances
Y11 0.190 0.027 0.000 0.140 0.248 *
Y12 0.206 0.029 0.000 0.156 0.272 *
Y13 0.187 0.024 0.000 0.144 0.240 *
Y14 0.191 0.029 0.000 0.142 0.254 *
Y21 0.221 0.029 0.000 0.168 0.286 *
Y22 0.228 0.030 0.000 0.179 0.294 *
Y23 0.187 0.030 0.000 0.137 0.254 *
Y24 0.153 0.023 0.000 0.112 0.203 *
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
NU
Y11 Y12 Y13 Y14 Y21
________ ________ ________ ________ ________
0 0 0 0 0
NU
Y22 Y23 Y24
________ ________ ________
0 0 0
LAMBDA
F1 F2 F1&1 F2&1
________ ________ ________ ________
Y11 0 0 0 0
Y12 1 0 0 0
Y13 2 0 0 0
Y14 3 0 0 0
Y21 0 0 0 0
Y22 0 4 0 0
Y23 0 5 0 0
Y24 0 6 0 0
THETA
Y11 Y12 Y13 Y14 Y21
________ ________ ________ ________ ________
Y11 7
Y12 0 8
Y13 0 0 9
Y14 0 0 0 10
Y21 0 0 0 0 11
Y22 0 0 0 0 0
Y23 0 0 0 0 0
Y24 0 0 0 0 0
THETA
Y22 Y23 Y24
________ ________ ________
Y22 12
Y23 0 13
Y24 0 0 14
ALPHA
F1 F2 F1&1 F2&1
________ ________ ________ ________
0 0 0 0
BETA
F1 F2 F1&1 F2&1
________ ________ ________ ________
F1 0 0 0 0
F2 0 0 0 0
F1&1 0 0 0 0
F2&1 0 0 0 0
PSI
F1 F2 F1&1 F2&1
________ ________ ________ ________
F1 15
F2 16 17
F1&1 0 0 0
F2&1 0 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN
NU
Y11 Y12 Y13 Y14 Y21
________ ________ ________ ________ ________
18 19 20 21 22
NU
Y22 Y23 Y24
________ ________ ________
23 24 25
LAMBDA
FB1 FB2 S11 S22 S12
________ ________ ________ ________ ________
Y11 26 0 0 0 0
Y12 27 0 0 0 0
Y13 28 0 0 0 0
Y14 29 0 0 0 0
Y21 0 30 0 0 0
Y22 0 31 0 0 0
Y23 0 32 0 0 0
Y24 0 33 0 0 0
LAMBDA
S21
________
Y11 0
Y12 0
Y13 0
Y14 0
Y21 0
Y22 0
Y23 0
Y24 0
THETA
Y11 Y12 Y13 Y14 Y21
________ ________ ________ ________ ________
Y11 34
Y12 0 35
Y13 0 0 36
Y14 0 0 0 37
Y21 0 0 0 0 38
Y22 0 0 0 0 0
Y23 0 0 0 0 0
Y24 0 0 0 0 0
THETA
Y22 Y23 Y24
________ ________ ________
Y22 39
Y23 0 40
Y24 0 0 41
ALPHA
FB1 FB2 S11 S22 S12
________ ________ ________ ________ ________
0 0 42 43 44
ALPHA
S21
________
45
BETA
FB1 FB2 S11 S22 S12
________ ________ ________ ________ ________
FB1 0 0 0 0 0
FB2 0 0 0 0 0
S11 0 0 0 0 0
S22 0 0 0 0 0
S12 0 0 0 0 0
S21 0 0 0 0 0
BETA
S21
________
FB1 0
FB2 0
S11 0
S22 0
S12 0
S21 0
PSI
FB1 FB2 S11 S22 S12
________ ________ ________ ________ ________
FB1 0
FB2 46 0
S11 47 48 49
S22 50 51 52 53
S12 54 55 56 57 58
S21 59 60 61 62 63
PSI
S21
________
S21 64
STARTING VALUES FOR WITHIN
NU
Y11 Y12 Y13 Y14 Y21
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
Y22 Y23 Y24
________ ________ ________
0.000 0.000 0.000
LAMBDA
F1 F2 F1&1 F2&1
________ ________ ________ ________
Y11 1.000 0.000 0.000 0.000
Y12 1.000 0.000 0.000 0.000
Y13 1.000 0.000 0.000 0.000
Y14 1.000 0.000 0.000 0.000
Y21 0.000 1.000 0.000 0.000
Y22 0.000 1.000 0.000 0.000
Y23 0.000 1.000 0.000 0.000
Y24 0.000 1.000 0.000 0.000
THETA
Y11 Y12 Y13 Y14 Y21
________ ________ ________ ________ ________
Y11 1.042
Y12 0.000 1.049
Y13 0.000 0.000 1.003
Y14 0.000 0.000 0.000 1.048
Y21 0.000 0.000 0.000 0.000 1.142
Y22 0.000 0.000 0.000 0.000 0.000
Y23 0.000 0.000 0.000 0.000 0.000
Y24 0.000 0.000 0.000 0.000 0.000
THETA
Y22 Y23 Y24
________ ________ ________
Y22 1.146
Y23 0.000 1.163
Y24 0.000 0.000 1.106
ALPHA
F1 F2 F1&1 F2&1
________ ________ ________ ________
0.000 0.000 0.000 0.000
BETA
F1 F2 F1&1 F2&1
________ ________ ________ ________
F1 0.000 0.000 0.000 0.000
F2 0.000 0.000 0.000 0.000
F1&1 0.000 0.000 0.000 0.000
F2&1 0.000 0.000 0.000 0.000
PSI
F1 F2 F1&1 F2&1
________ ________ ________ ________
F1 1.000
F2 0.000 1.000
F1&1 0.000 0.000 1.000
F2&1 0.000 0.000 0.000 1.000
STARTING VALUES FOR BETWEEN
NU
Y11 Y12 Y13 Y14 Y21
________ ________ ________ ________ ________
-0.046 -0.113 -0.039 -0.088 -0.032
NU
Y22 Y23 Y24
________ ________ ________
0.016 0.009 -0.034
LAMBDA
FB1 FB2 S11 S22 S12
________ ________ ________ ________ ________
Y11 1.000 0.000 0.000 0.000 0.000
Y12 1.000 0.000 0.000 0.000 0.000
Y13 1.000 0.000 0.000 0.000 0.000
Y14 1.000 0.000 0.000 0.000 0.000
Y21 0.000 1.000 0.000 0.000 0.000
Y22 0.000 1.000 0.000 0.000 0.000
Y23 0.000 1.000 0.000 0.000 0.000
Y24 0.000 1.000 0.000 0.000 0.000
LAMBDA
S21
________
Y11 0.000
Y12 0.000
Y13 0.000
Y14 0.000
Y21 0.000
Y22 0.000
Y23 0.000
Y24 0.000
THETA
Y11 Y12 Y13 Y14 Y21
________ ________ ________ ________ ________
Y11 1.042
Y12 0.000 1.049
Y13 0.000 0.000 1.003
Y14 0.000 0.000 0.000 1.048
Y21 0.000 0.000 0.000 0.000 1.142
Y22 0.000 0.000 0.000 0.000 0.000
Y23 0.000 0.000 0.000 0.000 0.000
Y24 0.000 0.000 0.000 0.000 0.000
THETA
Y22 Y23 Y24
________ ________ ________
Y22 1.146
Y23 0.000 1.163
Y24 0.000 0.000 1.106
ALPHA
FB1 FB2 S11 S22 S12
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
ALPHA
S21
________
0.000
BETA
FB1 FB2 S11 S22 S12
________ ________ ________ ________ ________
FB1 0.000 0.000 0.000 0.000 0.000
FB2 0.000 0.000 0.000 0.000 0.000
S11 0.000 0.000 0.000 0.000 0.000
S22 0.000 0.000 0.000 0.000 0.000
S12 0.000 0.000 0.000 0.000 0.000
S21 0.000 0.000 0.000 0.000 0.000
BETA
S21
________
FB1 0.000
FB2 0.000
S11 0.000
S22 0.000
S12 0.000
S21 0.000
PSI
FB1 FB2 S11 S22 S12
________ ________ ________ ________ ________
FB1 1.000
FB2 0.000 1.000
S11 0.000 0.000 1.000
S22 0.000 0.000 0.000 1.000
S12 0.000 0.000 0.000 0.000 1.000
S21 0.000 0.000 0.000 0.000 0.000
PSI
S21
________
S21 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~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~IG(-1.000,0.000) infinity infinity infinity
Parameter 8~IG(-1.000,0.000) infinity infinity infinity
Parameter 9~IG(-1.000,0.000) infinity infinity infinity
Parameter 10~IG(-1.000,0.000) infinity infinity infinity
Parameter 11~IG(-1.000,0.000) infinity infinity infinity
Parameter 12~IG(-1.000,0.000) infinity infinity infinity
Parameter 13~IG(-1.000,0.000) infinity infinity infinity
Parameter 14~IG(-1.000,0.000) infinity infinity infinity
Parameter 15~IW(0.000,-3) infinity infinity infinity
Parameter 16~IW(0.000,-3) infinity infinity infinity
Parameter 17~IW(0.000,-3) infinity 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~N(0.000,infinity) 0.0000 infinity infinity
Parameter 24~N(0.000,infinity) 0.0000 infinity infinity
Parameter 25~N(0.000,infinity) 0.0000 infinity infinity
Parameter 26~N(0.000,infinity) 0.0000 infinity infinity
Parameter 27~N(0.000,infinity) 0.0000 infinity infinity
Parameter 28~N(0.000,infinity) 0.0000 infinity infinity
Parameter 29~N(0.000,infinity) 0.0000 infinity infinity
Parameter 30~N(0.000,infinity) 0.0000 infinity infinity
Parameter 31~N(0.000,infinity) 0.0000 infinity infinity
Parameter 32~N(0.000,infinity) 0.0000 infinity infinity
Parameter 33~N(0.000,infinity) 0.0000 infinity infinity
Parameter 34~IG(-1.000,0.000) infinity infinity infinity
Parameter 35~IG(-1.000,0.000) infinity infinity infinity
Parameter 36~IG(-1.000,0.000) infinity infinity infinity
Parameter 37~IG(-1.000,0.000) infinity infinity infinity
Parameter 38~IG(-1.000,0.000) infinity infinity infinity
Parameter 39~IG(-1.000,0.000) infinity infinity infinity
Parameter 40~IG(-1.000,0.000) infinity infinity infinity
Parameter 41~IG(-1.000,0.000) infinity infinity infinity
Parameter 42~N(0.000,infinity) 0.0000 infinity infinity
Parameter 43~N(0.000,infinity) 0.0000 infinity infinity
Parameter 44~N(0.000,infinity) 0.0000 infinity infinity
Parameter 45~N(0.000,infinity) 0.0000 infinity infinity
Parameter 46~IW(0.000,-7)
Parameter 47~IW(0.000,-7)
Parameter 48~IW(0.000,-7)
Parameter 49~IW(0.000,-7)
Parameter 50~IW(0.000,-7)
Parameter 51~IW(0.000,-7)
Parameter 52~IW(0.000,-7)
Parameter 53~IW(0.000,-7)
Parameter 54~IW(0.000,-7)
Parameter 55~IW(0.000,-7)
Parameter 56~IW(0.000,-7)
Parameter 57~IW(0.000,-7)
Parameter 58~IW(0.000,-7)
Parameter 59~IW(0.000,-7)
Parameter 60~IW(0.000,-7)
Parameter 61~IW(0.000,-7)
Parameter 62~IW(0.000,-7)
Parameter 63~IW(0.000,-7)
Parameter 64~IW(0.000,-7)
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION
CHAIN BSEED
1 0
2 285380
POTENTIAL PARAMETER WITH
ITERATION SCALE REDUCTION HIGHEST PSR
100 1.170 51
200 1.315 51
300 1.131 26
400 1.173 25
500 1.048 22
600 1.034 30
700 1.034 30
800 1.041 24
900 1.070 60
1000 1.039 60
1100 1.045 60
1200 1.034 60
1300 1.024 60
1400 1.018 60
1500 1.018 60
1600 1.018 28
1700 1.024 25
1800 1.036 25
1900 1.039 25
2000 1.027 25
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: 23:37:39
Ending Time: 23:38:25
Elapsed Time: 00:00:46
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