Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:12 PM
INPUT INSTRUCTIONS
TITLE: this is an example of an N=1 time series analysis with a
first-order autoregressive AR(1) confirmatory factor
analysis (CFA) model with continuous factor indicators
DATA: FILE = ex6.26.dat;
VARIABLE: NAMES = y1-y4;
ANALYSIS: ESTIMATOR = BAYES;
PROCESSORS = 2;
BITERATIONS = (20000);
MODEL: f BY y1-y4 (&1);
y1-y4 ON f&1;
OUTPUT: TECH1 TECH8;
PLOT: TYPE = PLOT3;
INPUT READING TERMINATED NORMALLY
this is an example of an N=1 time series analysis with a
first-order autoregressive AR(1) confirmatory factor
analysis (CFA) model with continuous factor indicators
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 200
Number of dependent variables 4
Number of independent variables 0
Number of continuous latent variables 2
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4
Continuous latent variables
F F&1
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)
ex6.26.dat
Input data format FREE
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 0.096 -0.218 -3.443 0.50% -1.214 -0.218 0.115
200.000 2.000 -0.336 3.146 0.50% 0.456 1.287
Y2 0.179 0.096 -3.403 0.50% -0.965 -0.155 0.091
200.000 2.046 0.068 5.042 0.50% 0.437 1.375
Y3 0.160 -0.095 -4.141 0.50% -1.168 -0.345 0.030
200.000 2.424 -0.447 3.793 0.50% 0.552 1.612
Y4 0.130 -0.186 -4.430 0.50% -1.137 -0.125 0.301
200.000 2.313 0.074 4.586 0.50% 0.657 1.283
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 16
Information Criteria
Deviance (DIC) 2444.508
Estimated Number of Parameters (pD) 169.802
MODEL RESULTS
Posterior One-Tailed 95% C.I.
Estimate S.D. P-Value Lower 2.5% Upper 2.5% Significance
F BY
Y1 1.000 0.000 0.000 1.000 1.000
Y2 1.134 0.148 0.000 0.891 1.476 *
Y3 1.210 0.172 0.000 0.936 1.615 *
Y4 1.125 0.156 0.000 0.866 1.479 *
Y1 ON
F&1 0.299 0.137 0.008 0.056 0.589 *
Y2 ON
F&1 0.299 0.130 0.006 0.062 0.575 *
Y3 ON
F&1 0.401 0.139 0.001 0.149 0.696 *
Y4 ON
F&1 0.359 0.132 0.001 0.118 0.641 *
Intercepts
Y1 0.094 0.112 0.206 -0.127 0.314
Y2 0.177 0.117 0.065 -0.055 0.403
Y3 0.158 0.129 0.112 -0.100 0.404
Y4 0.127 0.123 0.152 -0.118 0.368
Variances
F 0.878 0.197 0.000 0.527 1.300 *
Residual Variances
Y1 1.020 0.137 0.000 0.786 1.320 *
Y2 0.883 0.133 0.000 0.646 1.171 *
Y3 1.052 0.156 0.000 0.774 1.388 *
Y4 1.136 0.155 0.000 0.870 1.473 *
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION
NU
Y1 Y2 Y3 Y4
________ ________ ________ ________
0 0 0 0
LAMBDA
F F&1 Y1 Y2 Y3
________ ________ ________ ________ ________
Y1 0 0 0 0 0
Y2 0 0 0 0 0
Y3 0 0 0 0 0
Y4 0 0 0 0 0
LAMBDA
Y4
________
Y1 0
Y2 0
Y3 0
Y4 0
THETA
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 0
Y2 0 0
Y3 0 0 0
Y4 0 0 0 0
ALPHA
F F&1 Y1 Y2 Y3
________ ________ ________ ________ ________
0 0 1 2 3
ALPHA
Y4
________
4
BETA
F F&1 Y1 Y2 Y3
________ ________ ________ ________ ________
F 0 0 0 0 0
F&1 0 0 0 0 0
Y1 0 5 0 0 0
Y2 6 7 0 0 0
Y3 8 9 0 0 0
Y4 10 11 0 0 0
BETA
Y4
________
F 0
F&1 0
Y1 0
Y2 0
Y3 0
Y4 0
PSI
F F&1 Y1 Y2 Y3
________ ________ ________ ________ ________
F 12
F&1 0 0
Y1 0 0 13
Y2 0 0 0 14
Y3 0 0 0 0 15
Y4 0 0 0 0 0
PSI
Y4
________
Y4 16
STARTING VALUES
NU
Y1 Y2 Y3 Y4
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
F F&1 Y1 Y2 Y3
________ ________ ________ ________ ________
Y1 0.000 0.000 1.000 0.000 0.000
Y2 0.000 0.000 0.000 1.000 0.000
Y3 0.000 0.000 0.000 0.000 1.000
Y4 0.000 0.000 0.000 0.000 0.000
LAMBDA
Y4
________
Y1 0.000
Y2 0.000
Y3 0.000
Y4 1.000
THETA
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 0.000
Y2 0.000 0.000
Y3 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000
ALPHA
F F&1 Y1 Y2 Y3
________ ________ ________ ________ ________
0.000 0.000 0.096 0.179 0.160
ALPHA
Y4
________
0.130
BETA
F F&1 Y1 Y2 Y3
________ ________ ________ ________ ________
F 0.000 0.000 0.000 0.000 0.000
F&1 0.000 0.000 0.000 0.000 0.000
Y1 1.000 0.000 0.000 0.000 0.000
Y2 1.000 0.000 0.000 0.000 0.000
Y3 1.000 0.000 0.000 0.000 0.000
Y4 1.000 0.000 0.000 0.000 0.000
BETA
Y4
________
F 0.000
F&1 0.000
Y1 0.000
Y2 0.000
Y3 0.000
Y4 0.000
PSI
F F&1 Y1 Y2 Y3
________ ________ ________ ________ ________
F 1.000
F&1 0.000 1.000
Y1 0.000 0.000 1.000
Y2 0.000 0.000 0.000 1.023
Y3 0.000 0.000 0.000 0.000 1.212
Y4 0.000 0.000 0.000 0.000 0.000
PSI
Y4
________
Y4 1.156
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~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~IG(-1.000,0.000) infinity infinity infinity
Parameter 16~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 2.761 12
200 1.117 9
300 1.375 7
400 1.056 7
500 1.036 13
600 1.041 4
700 1.027 4
800 1.008 11
900 1.010 12
1000 1.004 12
1100 1.018 8
1200 1.042 8
1300 1.016 8
1400 1.013 11
1500 1.016 11
1600 1.017 11
1700 1.012 11
1800 1.011 11
1900 1.017 11
2000 1.014 12
2100 1.031 12
2200 1.029 12
2300 1.020 12
2400 1.010 7
2500 1.015 12
2600 1.032 12
2700 1.043 12
2800 1.053 12
2900 1.045 12
3000 1.032 12
3100 1.031 12
3200 1.030 12
3300 1.027 12
3400 1.039 8
3500 1.041 8
3600 1.039 8
3700 1.034 6
3800 1.027 6
3900 1.025 8
4000 1.024 8
4100 1.021 8
4200 1.023 8
4300 1.024 8
4400 1.033 8
4500 1.032 8
4600 1.032 8
4700 1.034 8
4800 1.026 12
4900 1.026 12
5000 1.019 12
5100 1.017 12
5200 1.016 12
5300 1.021 12
5400 1.019 12
5500 1.019 12
5600 1.018 12
5700 1.021 12
5800 1.021 12
5900 1.024 12
6000 1.024 12
6100 1.022 12
6200 1.020 12
6300 1.019 12
6400 1.020 12
6500 1.013 12
6600 1.016 12
6700 1.014 12
6800 1.007 12
6900 1.007 12
7000 1.004 12
7100 1.003 12
7200 1.004 12
7300 1.004 12
7400 1.003 4
7500 1.005 12
7600 1.006 12
7700 1.007 12
7800 1.006 12
7900 1.006 12
8000 1.005 12
8100 1.005 12
8200 1.004 12
8300 1.005 12
8400 1.006 12
8500 1.005 12
8600 1.007 12
8700 1.006 12
8800 1.003 12
8900 1.002 12
9000 1.002 12
9100 1.002 12
9200 1.002 12
9300 1.001 5
9400 1.001 5
9500 1.001 5
9600 1.001 5
9700 1.001 12
9800 1.001 7
9900 1.001 5
10000 1.001 12
10100 1.001 12
10200 1.001 12
10300 1.002 12
10400 1.002 12
10500 1.001 12
10600 1.001 12
10700 1.001 12
10800 1.001 12
10900 1.002 12
11000 1.001 12
11100 1.001 12
11200 1.001 12
11300 1.001 12
11400 1.000 5
11500 1.000 5
11600 1.001 5
11700 1.001 5
11800 1.001 5
11900 1.001 5
12000 1.001 5
12100 1.001 15
12200 1.000 15
12300 1.000 5
12400 1.001 5
12500 1.000 14
12600 1.000 5
12700 1.000 5
12800 1.001 4
12900 1.001 12
13000 1.001 4
13100 1.002 4
13200 1.001 4
13300 1.001 4
13400 1.001 12
13500 1.001 4
13600 1.001 4
13700 1.001 4
13800 1.001 4
13900 1.002 4
14000 1.002 4
14100 1.002 12
14200 1.002 4
14300 1.003 4
14400 1.003 4
14500 1.003 4
14600 1.003 4
14700 1.004 4
14800 1.004 4
14900 1.003 4
15000 1.003 4
15100 1.004 4
15200 1.003 4
15300 1.004 4
15400 1.004 4
15500 1.004 4
15600 1.005 4
15700 1.005 4
15800 1.004 4
15900 1.004 4
16000 1.004 4
16100 1.004 4
16200 1.003 4
16300 1.003 4
16400 1.003 4
16500 1.003 4
16600 1.003 4
16700 1.003 4
16800 1.003 4
16900 1.003 4
17000 1.003 4
17100 1.003 4
17200 1.003 4
17300 1.004 4
17400 1.004 4
17500 1.004 4
17600 1.004 4
17700 1.005 4
17800 1.005 3
17900 1.006 3
18000 1.005 3
18100 1.005 3
18200 1.005 3
18300 1.005 3
18400 1.004 3
18500 1.004 3
18600 1.005 3
18700 1.004 3
18800 1.004 3
18900 1.004 3
19000 1.004 3
19100 1.004 3
19200 1.004 3
19300 1.004 3
19400 1.003 3
19500 1.003 3
19600 1.003 3
19700 1.003 3
19800 1.003 3
19900 1.003 3
20000 1.003 3
PLOT INFORMATION
The following plots are available:
Histograms (sample values)
Scatterplots (sample values)
Time series plots (sample values, ACF, PACF)
Bayesian posterior parameter distributions
Bayesian posterior parameter trace plots
Bayesian autocorrelation plots
Beginning Time: 23:12:29
Ending Time: 23:12:31
Elapsed Time: 00:00:02
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