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) IRT model for binary factor indicators
with random thresholds, a random AR(1) slope, and a random residual variance
DATA: FILE = ex9.35part2.dat;
VARIABLE: NAMES = u1-u4 subject;
CATEGORICAL = u1-u4;
CLUSTER = subject;
ANALYSIS: TYPE = TWOLEVEL RANDOM;
ESTIMATOR = BAYES;
PROCESSORS = 2;
BITERATIONS = (3000);
MODEL: %WITHIN%
f BY u1-u4*(&1 1-4);
s | f ON f&1;
logvf | f;
%BETWEEN%
fb BY u1-u4* (1-4);
[logvf@0];
fb s logvf WITH fb s logvf;
OUTPUT: TECH1 TECH8;
INPUT READING TERMINATED NORMALLY
this is an example of a two-level time series analysis
with a first-order autoregressive AR(1) IRT model for binary factor indicators
with random thresholds, 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
Binary and ordered categorical (ordinal)
U1 U2 U3 U4
Continuous latent variables
F F&1 FB S LOGVF
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
Link PROBIT
Input data file(s)
ex9.35part2.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 PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
U1
Category 1 0.484 9688.000
Category 2 0.516 10312.000
U2
Category 1 0.489 9775.000
Category 2 0.511 10225.000
U3
Category 1 0.497 9938.000
Category 2 0.503 10062.000
U4
Category 1 0.511 10222.000
Category 2 0.489 9778.000
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 19
MODEL RESULTS
Posterior One-Tailed 95% C.I.
Estimate S.D. P-Value Lower 2.5% Upper 2.5% Significance
Within Level
F BY
U1 0.964 0.027 0.000 0.913 1.020 *
U2 0.990 0.029 0.000 0.934 1.048 *
U3 1.009 0.027 0.000 0.958 1.064 *
U4 0.979 0.026 0.000 0.932 1.032 *
Between Level
FB BY
U1 0.964 0.027 0.000 0.913 1.020 *
U2 0.990 0.029 0.000 0.934 1.048 *
U3 1.009 0.027 0.000 0.958 1.064 *
U4 0.979 0.026 0.000 0.932 1.032 *
FB WITH
S -0.003 0.008 0.356 -0.019 0.013
LOGVF 0.002 0.017 0.464 -0.034 0.033
S WITH
LOGVF -0.005 0.007 0.215 -0.019 0.007
Means
S 0.293 0.016 0.000 0.260 0.324 *
LOGVF 0.000 0.000 1.000 0.000 0.000
Thresholds
U1$1 -0.067 0.048 0.082 -0.162 0.024
U2$1 -0.040 0.052 0.210 -0.145 0.054
U3$1 -0.014 0.053 0.399 -0.124 0.087
U4$1 0.038 0.050 0.221 -0.058 0.135
Variances
FB 0.165 0.028 0.000 0.116 0.224 *
S 0.030 0.004 0.000 0.023 0.039 *
LOGVF 0.111 0.022 0.000 0.076 0.161 *
Residual Variances
U1 0.280 0.040 0.000 0.212 0.368 *
U2 0.320 0.043 0.000 0.245 0.413 *
U3 0.340 0.046 0.000 0.262 0.441 *
U4 0.289 0.041 0.000 0.219 0.382 *
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
0 0 0 0
NU
U1 U2 U3 U4
________ ________ ________ ________
0 0 0 0
LAMBDA
F F&1
________ ________
U1 1 0
U2 2 0
U3 3 0
U4 4 0
THETA
U1 U2 U3 U4
________ ________ ________ ________
U1 0
U2 0 0
U3 0 0 0
U4 0 0 0 0
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
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
16 17 18 19
NU
U1 U2 U3 U4
________ ________ ________ ________
0 0 0 0
LAMBDA
FB S LOGVF
________ ________ ________
U1 1 0 0
U2 2 0 0
U3 3 0 0
U4 4 0 0
THETA
U1 U2 U3 U4
________ ________ ________ ________
U1 5
U2 0 6
U3 0 0 7
U4 0 0 0 8
ALPHA
FB S LOGVF
________ ________ ________
0 9 0
BETA
FB S LOGVF
________ ________ ________
FB 0 0 0
S 0 0 0
LOGVF 0 0 0
PSI
FB S LOGVF
________ ________ ________
FB 10
S 11 12
LOGVF 13 14 15
STARTING VALUES FOR WITHIN
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
0.000 0.000 0.000 0.000
NU
U1 U2 U3 U4
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
F F&1
________ ________
U1 1.000 0.000
U2 1.000 0.000
U3 1.000 0.000
U4 1.000 0.000
THETA
U1 U2 U3 U4
________ ________ ________ ________
U1 1.000
U2 0.000 1.000
U3 0.000 0.000 1.000
U4 0.000 0.000 0.000 1.000
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
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
-0.035 -0.025 -0.007 0.025
NU
U1 U2 U3 U4
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
FB S LOGVF
________ ________ ________
U1 1.000 0.000 0.000
U2 1.000 0.000 0.000
U3 1.000 0.000 0.000
U4 1.000 0.000 0.000
THETA
U1 U2 U3 U4
________ ________ ________ ________
U1 1.000
U2 0.000 1.000
U3 0.000 0.000 1.000
U4 0.000 0.000 0.000 1.000
ALPHA
FB S LOGVF
________ ________ ________
0.000 0.000 0.000
BETA
FB S LOGVF
________ ________ ________
FB 0.000 0.000 0.000
S 0.000 0.000 0.000
LOGVF 0.000 0.000 0.000
PSI
FB S LOGVF
________ ________ ________
FB 1.000
S 0.000 1.000
LOGVF 0.000 0.000 1.000
PRIORS FOR ALL PARAMETERS PRIOR MEAN PRIOR VARIANCE PRIOR STD. DEV.
Parameter 1~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 2~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 3~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 4~N(0.000,5.000) 0.0000 5.0000 2.2361
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~IG(-1.000,0.000) infinity infinity infinity
Parameter 9~N(0.000,infinity) 0.0000 infinity infinity
Parameter 10~IW(1.000,4) infinity infinity infinity
Parameter 11~IW(0.000,4) infinity infinity infinity
Parameter 12~IW(1.000,4) infinity infinity infinity
Parameter 13~IW(0.000,4) infinity infinity infinity
Parameter 14~IW(0.000,4) infinity infinity infinity
Parameter 15~IW(1.000,4) infinity infinity infinity
Parameter 16~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 17~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 18~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 19~N(0.000,5.000) 0.0000 5.0000 2.2361
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION
CHAIN BSEED
1 0
2 285380
POTENTIAL PARAMETER WITH
ITERATION SCALE REDUCTION HIGHEST PSR
100 2.908 2
200 1.779 15
300 1.919 15
400 1.541 15
500 1.339 2
600 1.086 10
700 1.063 10
800 1.094 4
900 1.070 2
1000 1.232 2
1100 1.144 2
1200 1.250 4
1300 1.225 4
1400 1.287 4
1500 1.287 4
1600 1.238 3
1700 1.282 3
1800 1.316 3
1900 1.190 3
2000 1.220 3
2100 1.228 3
2200 1.172 3
2300 1.134 3
2400 1.098 3
2500 1.131 3
2600 1.110 3
2700 1.067 2
2800 1.053 2
2900 1.047 2
3000 1.034 2
Beginning Time: 23:36:34
Ending Time: 23:37:39
Elapsed Time: 00:01:05
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