Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:33 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a two-level,
single-indicator measurement error model
analyzed as a two-level ARIMA(1,0,1) =
ARMA(1,1) with a random AR(1)
DATA: FILE = ex9.33.dat;
VARIABLE: NAMES = y subject;
CLUSTER = subject;
LAGGED = y(1);
ANALYSIS: TYPE = TWOLEVEL RANDOM;
ESTIMATOR = BAYES;
PROCESSORS = 2;
BITERATIONS = (5000);
MODEL: %WITHIN%
s | y ON y&1;
e BY y@1 (&1);
y@.01;
y ON e&1;
%BETWEEN%
y WITH s;
OUTPUT: TECH1 TECH8;
PLOT: TYPE = PLOT3;
INPUT READING TERMINATED NORMALLY
this is an example of a two-level,
single-indicator measurement error model
analyzed as a two-level ARIMA(1,0,1) =
ARMA(1,1) with a random AR(1)
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 20000
Number of dependent variables 1
Number of independent variables 1
Number of continuous latent variables 3
Observed dependent variables
Continuous
Y
Observed independent variables
Y&1
Continuous latent variables
E E&1 S
Variables with special functions
Cluster variable SUBJECT
Within variables
Y&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)
ex9.33.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
________
Y 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 0.021 -0.004 -5.636 0.01% -1.193 -0.345 0.012
20000.000 2.080 -0.006 5.161 0.01% 0.379 1.255
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 7
Information Criteria
Deviance (DIC) -30809.365
Estimated Number of Parameters (pD) 4543.140
MODEL RESULTS
Posterior One-Tailed 95% C.I.
Estimate S.D. P-Value Lower 2.5% Upper 2.5% Significance
Within Level
E BY
Y 1.000 0.000 0.000 1.000 1.000
Y ON
E&1 -0.100 0.025 0.000 -0.150 -0.047 *
Variances
E 1.539 0.016 0.000 1.509 1.570 *
Residual Variances
Y 0.010 0.000 0.000 0.010 0.010
Between Level
Y WITH
S -0.002 0.007 0.403 -0.017 0.013
Means
Y 0.022 0.049 0.319 -0.072 0.117
S 0.301 0.027 0.000 0.246 0.355 *
Variances
Y 0.441 0.049 0.000 0.358 0.549 *
S 0.012 0.003 0.000 0.008 0.018 *
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
NU
Y Y&1
________ ________
0 0
LAMBDA
E E&1 Y Y&1
________ ________ ________ ________
Y 0 0 0 0
Y&1 0 0 0 0
THETA
Y Y&1
________ ________
Y 0
Y&1 0 0
ALPHA
E E&1 Y Y&1
________ ________ ________ ________
0 0 0 0
BETA
E E&1 Y Y&1
________ ________ ________ ________
E 0 0 0 0
E&1 0 0 0 0
Y 0 1 0 0
Y&1 0 0 0 0
PSI
E E&1 Y Y&1
________ ________ ________ ________
E 2
E&1 0 0
Y 0 0 0
Y&1 0 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN
NU
Y
________
0
LAMBDA
S Y
________ ________
Y 0 0
THETA
Y
________
Y 0
ALPHA
S Y
________ ________
3 4
BETA
S Y
________ ________
S 0 0
Y 0 0
PSI
S Y
________ ________
S 5
Y 6 7
STARTING VALUES FOR WITHIN
NU
Y Y&1
________ ________
0.000 0.000
LAMBDA
E E&1 Y Y&1
________ ________ ________ ________
Y 0.000 0.000 1.000 0.000
Y&1 0.000 0.000 0.000 1.000
THETA
Y Y&1
________ ________
Y 0.000
Y&1 0.000 0.000
ALPHA
E E&1 Y Y&1
________ ________ ________ ________
0.000 0.000 0.000 0.000
BETA
E E&1 Y Y&1
________ ________ ________ ________
E 0.000 0.000 0.000 0.000
E&1 0.000 0.000 0.000 0.000
Y 1.000 0.000 0.000 0.000
Y&1 0.000 0.000 0.000 0.000
PSI
E E&1 Y Y&1
________ ________ ________ ________
E 1.000
E&1 0.000 1.000
Y 0.000 0.000 0.010
Y&1 0.000 0.000 0.000 1.041
STARTING VALUES FOR BETWEEN
NU
Y
________
0.000
LAMBDA
S Y
________ ________
Y 0.000 1.000
THETA
Y
________
Y 0.000
ALPHA
S Y
________ ________
0.000 0.021
BETA
S Y
________ ________
S 0.000 0.000
Y 0.000 0.000
PSI
S Y
________ ________
S 1.000
Y 0.000 1.040
PRIORS FOR ALL PARAMETERS PRIOR MEAN PRIOR VARIANCE PRIOR STD. DEV.
Parameter 1~N(0.000,infinity) 0.0000 infinity infinity
Parameter 2~IG(-1.000,0.000) infinity infinity infinity
Parameter 3~N(0.000,infinity) 0.0000 infinity infinity
Parameter 4~N(0.000,infinity) 0.0000 infinity infinity
Parameter 5~IW(0.000,-3) infinity infinity infinity
Parameter 6~IW(0.000,-3) infinity infinity infinity
Parameter 7~IW(0.000,-3) 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 1.070 3
200 1.302 3
300 1.383 3
400 1.463 3
500 1.428 3
600 1.362 3
700 1.325 3
800 1.207 3
900 1.133 6
1000 1.047 7
1100 1.028 7
1200 1.010 7
1300 1.031 1
1400 1.028 1
1500 1.036 6
1600 1.030 6
1700 1.034 3
1800 1.043 3
1900 1.041 3
2000 1.051 1
2100 1.063 1
2200 1.063 3
2300 1.073 1
2400 1.093 1
2500 1.112 1
2600 1.125 1
2700 1.137 1
2800 1.131 1
2900 1.114 1
3000 1.089 1
3100 1.067 1
3200 1.056 6
3300 1.050 6
3400 1.045 6
3500 1.033 6
3600 1.018 6
3700 1.005 6
3800 1.001 3
3900 1.006 3
4000 1.012 3
4100 1.021 3
4200 1.030 3
4300 1.041 3
4400 1.054 3
4500 1.072 3
4600 1.094 3
4700 1.118 3
4800 1.142 3
4900 1.170 3
5000 1.199 3
5100 1.217 3
5200 1.246 3
5300 1.282 3
5400 1.315 3
5500 1.348 1
5600 1.382 1
5700 1.406 1
5800 1.402 1
5900 1.388 1
6000 1.372 1
6100 1.360 1
6200 1.348 1
6300 1.337 1
6400 1.331 1
6500 1.326 1
6600 1.326 1
6700 1.332 1
6800 1.346 1
6900 1.363 3
7000 1.380 3
7100 1.390 3
7200 1.401 3
7300 1.413 3
7400 1.420 3
7500 1.435 3
7600 1.448 3
7700 1.454 3
7800 1.461 3
7900 1.481 3
8000 1.509 3
8100 1.529 3
8200 1.550 3
8300 1.571 3
8400 1.588 3
8500 1.599 3
8600 1.593 1
8700 1.563 1
8800 1.508 1
8900 1.438 1
9000 1.370 1
9100 1.308 1
9200 1.262 1
9300 1.228 1
9400 1.191 1
9500 1.155 1
9600 1.123 1
9700 1.098 1
9800 1.075 1
9900 1.057 1
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: 23:33:36
Ending Time: 23:36:04
Elapsed Time: 00:02:28
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