Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:52 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a cross-classified time series analysis
with a first-order autoregressive AR(1) confirmatory factor analysis (CFA) model
for continuous factor indicators with random intercepts and a factor varying
across both subjects and time
DATA: FILE = ex9.40.dat;
VARIABLE: NAMES = y1-y3 time subject;
CLUSTER = subject time;
ANALYSIS: TYPE = CROSSCLASSIFIED RANDOM;
ESTIMATOR = BAYES;
PROCESSORS = 2;
BITERATIONS = (1000);
MODEL: %WITHIN%
f BY y1-y3* (&1 1-3);
f@1;
f ON f&1;
%BETWEEN subject%
fsubj BY y1-y3* (1-3);
%BETWEEN time%
ftime BY y1-y3* (1-3);
OUTPUT: TECH1 TECH8;
PLOT: TYPE = PLOT3;
FACTORS = ALL;
INPUT READING TERMINATED NORMALLY
this is an example of a cross-classified time series analysis
with a first-order autoregressive AR(1) confirmatory factor analysis (CFA) model
for continuous factor indicators with random intercepts and a factor varying
across both subjects and time
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 20000
Number of dependent variables 3
Number of independent variables 0
Number of continuous latent variables 4
Observed dependent variables
Continuous
Y1 Y2 Y3
Continuous latent variables
F F&1 FTIME FSUBJ
Variables with special functions
Cluster variables SUBJECT TIME
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
Specifications for Bayes Factor Score Estimation
Number of imputed data sets 50
Iteration intervals for thinning 1
Input data file(s)
ex9.40.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
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 0.940 -0.020 -10.014 0.01% -1.121 0.321 0.949
20000.000 5.992 -0.006 10.079 0.01% 1.564 3.014
Y2 0.954 -0.030 -8.184 0.01% -1.137 0.344 0.958
20000.000 6.262 -0.016 9.991 0.01% 1.589 3.070
Y3 0.783 0.045 -7.819 0.01% -1.366 0.133 0.792
20000.000 6.434 -0.013 11.156 0.01% 1.419 2.886
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 18
Information Criteria
Deviance (DIC) 197729.437
Estimated Number of Parameters (pD) 16490.195
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 1.280 0.011 0.000 1.258 1.300 *
Y2 1.296 0.011 0.000 1.276 1.317 *
Y3 1.268 0.011 0.000 1.246 1.289 *
F ON
F&1 0.299 0.008 0.000 0.282 0.316 *
Residual Variances
Y1 1.198 0.018 0.000 1.163 1.234 *
Y2 1.173 0.018 0.000 1.137 1.208 *
Y3 1.232 0.017 0.000 1.197 1.266 *
F 1.000 0.000 0.000 1.000 1.000
Between TIME Level
FTIME BY
Y1 1.280 0.011 0.000 1.258 1.300 *
Y2 1.296 0.011 0.000 1.276 1.317 *
Y3 1.268 0.011 0.000 1.246 1.289 *
Variances
FTIME 0.617 0.103 0.000 0.452 0.849 *
Residual Variances
Y1 0.129 0.049 0.000 0.049 0.242 *
Y2 0.367 0.073 0.000 0.244 0.532 *
Y3 0.353 0.071 0.000 0.235 0.516 *
Between SUBJECT Level
FSUBJ BY
Y1 1.280 0.011 0.000 1.258 1.300 *
Y2 1.296 0.011 0.000 1.276 1.317 *
Y3 1.268 0.011 0.000 1.246 1.289 *
Intercepts
Y1 0.985 0.187 0.000 0.573 1.289 *
Y2 1.022 0.169 0.000 0.609 1.273 *
Y3 0.828 0.164 0.000 0.494 1.138 *
Variances
FSUBJ 0.890 0.108 0.000 0.713 1.132 *
Residual Variances
Y1 0.538 0.082 0.000 0.397 0.706 *
Y2 0.502 0.082 0.000 0.369 0.679 *
Y3 0.588 0.088 0.000 0.443 0.782 *
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
NU
Y1 Y2 Y3
________ ________ ________
0 0 0
LAMBDA
F F&1
________ ________
Y1 1 0
Y2 2 0
Y3 3 0
THETA
Y1 Y2 Y3
________ ________ ________
Y1 4
Y2 0 5
Y3 0 0 6
ALPHA
F F&1
________ ________
0 0
BETA
F F&1
________ ________
F 0 7
F&1 0 0
PSI
F F&1
________ ________
F 0
F&1 0 0
PARAMETER SPECIFICATION FOR BETWEEN TIME
NU
Y1 Y2 Y3
________ ________ ________
0 0 0
LAMBDA
FTIME
________
Y1 1
Y2 2
Y3 3
THETA
Y1 Y2 Y3
________ ________ ________
Y1 8
Y2 0 9
Y3 0 0 10
ALPHA
FTIME
________
0
BETA
FTIME
________
FTIME 0
PSI
FTIME
________
FTIME 11
PARAMETER SPECIFICATION FOR BETWEEN SUBJECT
NU
Y1 Y2 Y3
________ ________ ________
12 13 14
LAMBDA
FSUBJ
________
Y1 1
Y2 2
Y3 3
THETA
Y1 Y2 Y3
________ ________ ________
Y1 15
Y2 0 16
Y3 0 0 17
ALPHA
FSUBJ
________
0
BETA
FSUBJ
________
FSUBJ 0
PSI
FSUBJ
________
FSUBJ 18
STARTING VALUES FOR WITHIN
NU
Y1 Y2 Y3
________ ________ ________
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
THETA
Y1 Y2 Y3
________ ________ ________
Y1 2.996
Y2 0.000 3.131
Y3 0.000 0.000 3.217
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 1.000
F&1 0.000 1.000
STARTING VALUES FOR BETWEEN TIME
NU
Y1 Y2 Y3
________ ________ ________
0.000 0.000 0.000
LAMBDA
FTIME
________
Y1 1.000
Y2 1.000
Y3 1.000
THETA
Y1 Y2 Y3
________ ________ ________
Y1 2.996
Y2 0.000 3.131
Y3 0.000 0.000 3.217
ALPHA
FTIME
________
0.000
BETA
FTIME
________
FTIME 0.000
PSI
FTIME
________
FTIME 1.000
STARTING VALUES FOR BETWEEN SUBJECT
NU
Y1 Y2 Y3
________ ________ ________
0.940 0.954 0.783
LAMBDA
FSUBJ
________
Y1 1.000
Y2 1.000
Y3 1.000
THETA
Y1 Y2 Y3
________ ________ ________
Y1 2.996
Y2 0.000 3.131
Y3 0.000 0.000 3.217
ALPHA
FSUBJ
________
0.000
BETA
FSUBJ
________
FSUBJ 0.000
PSI
FSUBJ
________
FSUBJ 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~N(0.000,infinity) 0.0000 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~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~IG(-1.000,0.000) infinity 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
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION
CHAIN BSEED
1 0
2 285380
POTENTIAL PARAMETER WITH
ITERATION SCALE REDUCTION HIGHEST PSR
100 1.178 16
200 1.178 8
300 1.282 13
400 1.445 13
500 1.453 14
600 1.536 14
700 1.789 14
800 1.673 14
900 1.846 14
1000 2.036 14
1100 2.333 12
1200 2.298 12
1300 2.065 12
1400 1.692 12
1500 1.400 12
1600 1.216 12
1700 1.069 13
SUMMARIES OF PLAUSIBLE VALUES (N = NUMBER OF OBSERVATIONS * NUMBER OF IMPUTATIONS)
SAMPLE STATISTICS
Means
F F&1 FTIME FSUBJ B2a_Y1
________ ________ ________ ________ ________
-0.006 -0.006 0.029 0.004 0.050
Means
B2a_Y2 B2a_Y3 B2b_Y1 B2b_Y2 B2b_Y3
________ ________ ________ ________ ________
0.003 0.022 0.897 0.961 0.771
Covariances
F F&1 FTIME FSUBJ B2a_Y1
________ ________ ________ ________ ________
F 1.100
F&1 0.328 1.100
FTIME -0.004 -0.004 0.606
FSUBJ -0.001 -0.001 0.000 0.888
B2a_Y1 -0.005 -0.005 0.755 0.000 1.059
B2a_Y2 -0.007 -0.006 0.784 0.000 0.971
B2a_Y3 -0.004 -0.009 0.807 0.000 1.001
B2b_Y1 -0.003 -0.004 0.000 1.117 -0.001
B2b_Y2 -0.002 -0.003 0.000 1.120 0.000
B2b_Y3 0.004 0.004 0.000 1.134 0.000
Covariances
B2a_Y2 B2a_Y3 B2b_Y1 B2b_Y2 B2b_Y3
________ ________ ________ ________ ________
B2a_Y2 1.376
B2a_Y3 1.070 1.397
B2b_Y1 0.000 0.001 1.960
B2b_Y2 -0.001 -0.001 1.410 1.893
B2b_Y3 -0.001 -0.001 1.465 1.433 2.044
Correlations
F F&1 FTIME FSUBJ B2a_Y1
________ ________ ________ ________ ________
F 1.000
F&1 0.298 1.000
FTIME -0.005 -0.005 1.000
FSUBJ -0.001 -0.001 0.000 1.000
B2a_Y1 -0.005 -0.005 0.942 0.001 1.000
B2a_Y2 -0.006 -0.005 0.858 0.000 0.804
B2a_Y3 -0.003 -0.007 0.877 0.000 0.823
B2b_Y1 -0.002 -0.003 0.000 0.847 0.000
B2b_Y2 -0.001 -0.002 0.000 0.864 0.000
B2b_Y3 0.003 0.003 0.000 0.842 0.000
Correlations
B2a_Y2 B2a_Y3 B2b_Y1 B2b_Y2 B2b_Y3
________ ________ ________ ________ ________
B2a_Y2 1.000
B2a_Y3 0.772 1.000
B2b_Y1 0.000 0.000 1.000
B2b_Y2 -0.001 0.000 0.732 1.000
B2b_Y3 0.000 -0.001 0.732 0.729 1.000
SUMMARY OF PLAUSIBLE STANDARD DEVIATION (N = NUMBER OF OBSERVATIONS)
SAMPLE STATISTICS
Means
F_SD F&1_SD FTIME_SD FSUBJ_SD B2a_Y1_S
________ ________ ________ ________ ________
0.456 0.462 0.213 0.339 0.113
Means
B2a_Y2_S B2a_Y3_S B2b_Y1_S B2b_Y2_S B2b_Y3_S
________ ________ ________ ________ ________
0.117 0.120 0.181 0.182 0.183
Covariances
F_SD F&1_SD FTIME_SD FSUBJ_SD B2a_Y1_S
________ ________ ________ ________ ________
F_SD 0.002
F&1_SD 0.000 0.005
FTIME_SD 0.000 0.000 0.001
FSUBJ_SD 0.000 0.000 0.000 0.001
B2a_Y1_S 0.000 0.000 0.000 0.000 0.000
B2a_Y2_S 0.000 0.000 0.000 0.000 0.000
B2a_Y3_S 0.000 0.000 0.000 0.000 0.000
B2b_Y1_S 0.000 0.000 0.000 0.000 0.000
B2b_Y2_S 0.000 0.000 0.000 0.000 0.000
B2b_Y3_S 0.000 0.000 0.000 0.000 0.000
Covariances
B2a_Y2_S B2a_Y3_S B2b_Y1_S B2b_Y2_S B2b_Y3_S
________ ________ ________ ________ ________
B2a_Y2_S 0.000
B2a_Y3_S 0.000 0.000
B2b_Y1_S 0.000 0.000 0.001
B2b_Y2_S 0.000 0.000 0.001 0.001
B2b_Y3_S 0.000 0.000 0.001 0.001 0.001
Correlations
F_SD F&1_SD FTIME_SD FSUBJ_SD B2a_Y1_S
________ ________ ________ ________ ________
F_SD 1.000
F&1_SD 0.037 1.000
FTIME_SD 0.007 -0.021 1.000
FSUBJ_SD 0.049 0.035 0.000 1.000
B2a_Y1_S 0.029 -0.040 0.199 0.000 1.000
B2a_Y2_S 0.019 0.019 0.024 0.000 0.572
B2a_Y3_S 0.027 0.103 0.038 0.000 0.437
B2b_Y1_S 0.149 0.092 0.000 0.275 0.000
B2b_Y2_S 0.139 0.086 0.000 0.267 0.000
B2b_Y3_S 0.133 0.082 0.000 0.310 0.000
Correlations
B2a_Y2_S B2a_Y3_S B2b_Y1_S B2b_Y2_S B2b_Y3_S
________ ________ ________ ________ ________
B2a_Y2_S 1.000
B2a_Y3_S 0.614 1.000
B2b_Y1_S 0.000 0.000 1.000
B2b_Y2_S 0.000 0.000 0.804 1.000
B2b_Y3_S 0.000 0.000 0.758 0.827 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: 23:52:34
Ending Time: 23:55:10
Elapsed Time: 00:02:36
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