Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:05 PM
INPUT INSTRUCTIONS
TITLE: this is an example of multiple imputation of
plausible values generated from a multiple
indicator linear growth model for categorical
outcomes using Bayesian estimation
DATA: FILE = ex11.7.dat;
VARIABLE: NAMES = u11 u21 u31 u12 u22 u32 u13 u23 u33;
CATEGORICAL = u11-u33;
ANALYSIS: ESTIMATOR = BAYES;
PROCESSORS = 2;
MODEL: f1 BY u11
u21-u31 (1-2);
f2 BY u12
u22-u32 (1-2);
f3 BY u13
u23-u33 (1-2);
[u11$1 u12$1 u13$1] (3);
[u21$1 u22$1 u23$1] (4);
[u31$1 u32$1 u33$1] (5);
i s | f1@0 f2@1 f3@2;
DATA IMPUTATION:
NDATASETS = 20;
SAVE = ex11.7imp*.dat;
OUTPUT: TECH1 TECH8;
SAVEDATA: FILE = ex11.7plaus.dat;
SAVE = FSCORES(20) LRESPONSES;
INPUT READING TERMINATED NORMALLY
this is an example of multiple imputation of
plausible values generated from a multiple
indicator linear growth model for categorical
outcomes using Bayesian estimation
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 500
Number of replications
Requested 20
Completed 20
Number of dependent variables 9
Number of independent variables 0
Number of continuous latent variables 5
Observed dependent variables
Binary and ordered categorical (ordinal)
U11 U21 U31 U12 U22 U32
U13 U23 U33
Continuous latent variables
F1 F2 F3 I S
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
Specifications for Data Imputation
Number of imputed data sets 20
Iteration intervals for thinning 100
Input data file(s)
ex11.7.dat
Input data format FREE
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
U11
Category 1 0.310 155.000
Category 2 0.690 345.000
U21
Category 1 0.502 251.000
Category 2 0.498 249.000
U31
Category 1 0.642 321.000
Category 2 0.358 179.000
U12
Category 1 0.124 62.000
Category 2 0.876 438.000
U22
Category 1 0.218 109.000
Category 2 0.782 391.000
U32
Category 1 0.312 156.000
Category 2 0.688 344.000
U13
Category 1 0.028 14.000
Category 2 0.972 486.000
U23
Category 1 0.072 36.000
Category 2 0.928 464.000
U33
Category 1 0.130 65.000
Category 2 0.870 435.000
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 12
Bayesian Posterior Predictive Checking using Chi-Square
95% Confidence Interval for the Difference Between
the Observed and the Replicated Chi-Square Values
-27.846 29.682
Posterior Predictive P-Value 0.493
MODEL RESULTS
Posterior One-Tailed 95% C.I.
Estimate S.D. P-Value Lower 2.5% Upper 2.5% Significance
I |
F1 1.000 0.000 0.000 1.000 1.000
F2 1.000 0.000 0.000 1.000 1.000
F3 1.000 0.000 0.000 1.000 1.000
S |
F1 0.000 0.000 1.000 0.000 0.000
F2 1.000 0.000 0.000 1.000 1.000
F3 2.000 0.000 0.000 2.000 2.000
F1 BY
U11 1.000 0.000 0.000 1.000 1.000
U21 1.081 0.120 0.000 0.859 1.340 *
U31 1.147 0.138 0.000 0.911 1.423 *
F2 BY
U12 1.000 0.000 0.000 1.000 1.000
U22 1.081 0.120 0.000 0.859 1.340 *
U32 1.147 0.138 0.000 0.911 1.423 *
F3 BY
U13 1.000 0.000 0.000 1.000 1.000
U23 1.081 0.120 0.000 0.859 1.340 *
U33 1.147 0.138 0.000 0.911 1.423 *
S WITH
I -0.121 0.074 0.004 -0.301 -0.015 *
Means
I 0.000 0.000 1.000 0.000 0.000
S 0.930 0.061 0.000 0.822 1.058 *
Intercepts
F1 0.000 0.000 1.000 0.000 0.000
F2 0.000 0.000 1.000 0.000 0.000
F3 0.000 0.000 1.000 0.000 0.000
Thresholds
U11$1 -0.661 0.067 0.000 -0.799 -0.534 *
U21$1 -0.017 0.071 0.400 -0.149 0.130
U31$1 0.488 0.093 0.000 0.320 0.676 *
U12$1 -0.661 0.067 0.000 -0.799 -0.534 *
U22$1 -0.017 0.071 0.400 -0.149 0.130
U32$1 0.488 0.093 0.000 0.320 0.676 *
U13$1 -0.661 0.067 0.000 -0.799 -0.534 *
U23$1 -0.017 0.071 0.400 -0.149 0.130
U33$1 0.488 0.093 0.000 0.320 0.676 *
Variances
I 0.535 0.144 0.000 0.298 0.839 *
S 0.076 0.051 0.000 0.026 0.216 *
Residual Variances
F1 0.496 0.182 0.000 0.178 0.912 *
F2 0.391 0.114 0.000 0.196 0.658 *
F3 0.438 0.199 0.000 0.054 0.792 *
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION
TAU
U11$1 U21$1 U31$1 U12$1 U22$1
________ ________ ________ ________ ________
10 11 12 10 11
TAU
U32$1 U13$1 U23$1 U33$1
________ ________ ________ ________
12 10 11 12
NU
U11 U21 U31 U12 U22
________ ________ ________ ________ ________
0 0 0 0 0
NU
U32 U13 U23 U33
________ ________ ________ ________
0 0 0 0
LAMBDA
F1 F2 F3 I S
________ ________ ________ ________ ________
U11 0 0 0 0 0
U21 1 0 0 0 0
U31 2 0 0 0 0
U12 0 0 0 0 0
U22 0 1 0 0 0
U32 0 2 0 0 0
U13 0 0 0 0 0
U23 0 0 1 0 0
U33 0 0 2 0 0
THETA
U11 U21 U31 U12 U22
________ ________ ________ ________ ________
U11 0
U21 0 0
U31 0 0 0
U12 0 0 0 0
U22 0 0 0 0 0
U32 0 0 0 0 0
U13 0 0 0 0 0
U23 0 0 0 0 0
U33 0 0 0 0 0
THETA
U32 U13 U23 U33
________ ________ ________ ________
U32 0
U13 0 0
U23 0 0 0
U33 0 0 0 0
ALPHA
F1 F2 F3 I S
________ ________ ________ ________ ________
0 0 0 0 3
BETA
F1 F2 F3 I S
________ ________ ________ ________ ________
F1 0 0 0 0 0
F2 0 0 0 0 0
F3 0 0 0 0 0
I 0 0 0 0 0
S 0 0 0 0 0
PSI
F1 F2 F3 I S
________ ________ ________ ________ ________
F1 4
F2 0 5
F3 0 0 6
I 0 0 0 7
S 0 0 0 8 9
STARTING VALUES
TAU
U11$1 U21$1 U31$1 U12$1 U22$1
________ ________ ________ ________ ________
-1.167 -0.708 -0.390 -1.167 -0.708
TAU
U32$1 U13$1 U23$1 U33$1
________ ________ ________ ________
-0.390 -1.167 -0.708 -0.390
NU
U11 U21 U31 U12 U22
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
U32 U13 U23 U33
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
F1 F2 F3 I S
________ ________ ________ ________ ________
U11 1.000 0.000 0.000 0.000 0.000
U21 1.000 0.000 0.000 0.000 0.000
U31 1.000 0.000 0.000 0.000 0.000
U12 0.000 1.000 0.000 0.000 0.000
U22 0.000 1.000 0.000 0.000 0.000
U32 0.000 1.000 0.000 0.000 0.000
U13 0.000 0.000 1.000 0.000 0.000
U23 0.000 0.000 1.000 0.000 0.000
U33 0.000 0.000 1.000 0.000 0.000
THETA
U11 U21 U31 U12 U22
________ ________ ________ ________ ________
U11 1.000
U21 0.000 1.000
U31 0.000 0.000 1.000
U12 0.000 0.000 0.000 1.000
U22 0.000 0.000 0.000 0.000 1.000
U32 0.000 0.000 0.000 0.000 0.000
U13 0.000 0.000 0.000 0.000 0.000
U23 0.000 0.000 0.000 0.000 0.000
U33 0.000 0.000 0.000 0.000 0.000
THETA
U32 U13 U23 U33
________ ________ ________ ________
U32 1.000
U13 0.000 1.000
U23 0.000 0.000 1.000
U33 0.000 0.000 0.000 1.000
ALPHA
F1 F2 F3 I S
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
BETA
F1 F2 F3 I S
________ ________ ________ ________ ________
F1 0.000 0.000 0.000 1.000 0.000
F2 0.000 0.000 0.000 1.000 1.000
F3 0.000 0.000 0.000 1.000 2.000
I 0.000 0.000 0.000 0.000 0.000
S 0.000 0.000 0.000 0.000 0.000
PSI
F1 F2 F3 I S
________ ________ ________ ________ ________
F1 1.000
F2 0.000 1.000
F3 0.000 0.000 1.000
I 0.000 0.000 0.000 1.000
S 0.000 0.000 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,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~IW(0.000,-3) infinity infinity infinity
Parameter 8~IW(0.000,-3) infinity infinity infinity
Parameter 9~IW(0.000,-3) infinity infinity infinity
Parameter 10~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 11~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 12~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 2.764 2
200 3.037 3
300 2.611 1
400 2.371 3
500 2.673 3
600 2.399 3
700 2.296 3
800 1.797 3
900 1.874 3
1000 1.933 3
1100 2.268 3
1200 2.224 3
1300 1.821 3
1400 1.482 3
1500 1.573 3
1600 1.708 3
1700 1.731 3
1800 1.648 3
1900 1.491 3
2000 1.263 3
2100 1.187 3
2200 1.160 3
2300 1.111 6
2400 1.095 9
2500 1.102 6
2600 1.121 6
2700 1.118 6
2800 1.097 6
2900 1.078 6
SUMMARIES OF PLAUSIBLE VALUES (N = NUMBER OF OBSERVATIONS * NUMBER OF IMPUTATIONS)
SAMPLE STATISTICS
Means
U11* U21* U31* U12* U22*
________ ________ ________ ________ ________
0.022 -0.012 -0.042 0.931 1.058
Means
U32* U13* U23* U33* F1
________ ________ ________ ________ ________
1.101 1.887 2.055 2.097 -0.008
Means
F2 F3 I S
________ ________ ________ ________
0.966 1.898 -0.001 0.959
Covariances
U11* U21* U31* U12* U22*
________ ________ ________ ________ ________
U11* 2.056
U21* 1.134 2.200
U31* 1.162 1.246 2.272
U12* 0.450 0.421 0.492 1.838
U22* 0.445 0.489 0.534 0.861 1.912
U32* 0.433 0.473 0.510 0.836 0.919
U13* 0.350 0.378 0.400 0.308 0.334
U23* 0.350 0.344 0.404 0.307 0.359
U33* 0.372 0.384 0.403 0.357 0.363
F1 1.036 1.110 1.132 0.429 0.456
F2 0.438 0.453 0.504 0.811 0.858
F3 0.316 0.332 0.367 0.312 0.325
I 0.592 0.624 0.643 0.433 0.463
S -0.147 -0.151 -0.155 -0.062 -0.068
Covariances
U32* U13* U23* U33* F1
________ ________ ________ ________ ________
U32* 1.911
U13* 0.346 1.855
U23* 0.381 0.920 2.020
U33* 0.380 0.962 1.018 2.132
F1 0.440 0.343 0.331 0.348 1.017
F2 0.849 0.315 0.326 0.348 0.429
F3 0.332 0.864 0.910 0.943 0.307
I 0.457 0.329 0.337 0.351 0.581
S -0.069 -0.002 -0.005 -0.003 -0.142
Covariances
F2 F3 I S
________ ________ ________ ________
F2 0.804
F3 0.308 0.854
I 0.432 0.308 0.583
S -0.063 0.004 -0.142 0.075
Correlations
U11* U21* U31* U12* U22*
________ ________ ________ ________ ________
U11* 1.000
U21* 0.533 1.000
U31* 0.538 0.557 1.000
U12* 0.232 0.209 0.241 1.000
U22* 0.224 0.239 0.256 0.459 1.000
U32* 0.218 0.231 0.245 0.446 0.481
U13* 0.179 0.187 0.195 0.167 0.177
U23* 0.172 0.163 0.189 0.160 0.183
U33* 0.178 0.177 0.183 0.180 0.180
F1 0.716 0.742 0.745 0.313 0.327
F2 0.341 0.341 0.373 0.667 0.692
F3 0.238 0.243 0.263 0.249 0.255
I 0.541 0.551 0.559 0.419 0.438
S -0.373 -0.371 -0.374 -0.166 -0.178
Correlations
U32* U13* U23* U33* F1
________ ________ ________ ________ ________
U32* 1.000
U13* 0.184 1.000
U23* 0.194 0.475 1.000
U33* 0.188 0.484 0.490 1.000
F1 0.315 0.250 0.231 0.236 1.000
F2 0.685 0.258 0.256 0.266 0.475
F3 0.260 0.687 0.693 0.699 0.329
I 0.433 0.317 0.310 0.315 0.754
S -0.180 -0.004 -0.012 -0.008 -0.513
Correlations
F2 F3 I S
________ ________ ________ ________
F2 1.000
F3 0.372 1.000
I 0.632 0.436 1.000
S -0.255 0.018 -0.675 1.000
SUMMARY OF PLAUSIBLE STANDARD DEVIATION (N = NUMBER OF OBSERVATIONS)
SAMPLE STATISTICS
Means
U11*_SD U21*_SD U31*_SD U12*_SD U22*_SD
________ ________ ________ ________ ________
0.831 0.818 0.853 0.958 0.882
Means
U32*_SD U13*_SD U23*_SD U33*_SD F1_SD
________ ________ ________ ________ ________
0.827 1.156 1.128 1.077 0.612
Means
F2_SD F3_SD I_SD S_SD
________ ________ ________ ________
0.619 0.741 0.563 0.247
Covariances
U11*_SD U21*_SD U31*_SD U12*_SD U22*_SD
________ ________ ________ ________ ________
U11*_SD 0.047
U21*_SD 0.017 0.042
U31*_SD 0.001 0.017 0.044
U12*_SD 0.010 -0.001 -0.007 0.059
U22*_SD 0.012 0.005 -0.003 0.029 0.058
U32*_SD 0.011 0.006 0.001 0.018 0.023
U13*_SD 0.004 -0.005 -0.010 0.012 0.013
U23*_SD 0.008 -0.001 -0.006 0.014 0.013
U33*_SD 0.009 -0.004 -0.006 0.017 0.014
F1_SD 0.009 0.011 0.010 0.001 0.003
F2_SD 0.005 0.002 0.000 0.014 0.016
F3_SD 0.006 -0.001 -0.003 0.008 0.006
I_SD 0.005 0.005 0.003 0.002 0.003
S_SD 0.001 0.001 0.001 0.000 -0.001
Covariances
U32*_SD U13*_SD U23*_SD U33*_SD F1_SD
________ ________ ________ ________ ________
U32*_SD 0.050
U13*_SD 0.007 0.059
U23*_SD 0.012 0.028 0.070
U33*_SD 0.013 0.033 0.036 0.085
F1_SD 0.004 -0.002 0.001 0.003 0.015
F2_SD 0.014 0.004 0.006 0.008 0.002
F3_SD 0.006 0.021 0.023 0.026 0.001
I_SD 0.003 0.001 0.002 0.004 0.005
S_SD 0.001 -0.001 0.000 0.000 0.001
Covariances
F2_SD F3_SD I_SD S_SD
________ ________ ________ ________
F2_SD 0.016
F3_SD 0.004 0.023
I_SD 0.003 0.002 0.010
S_SD 0.000 0.000 0.002 0.002
Correlations
U11*_SD U21*_SD U31*_SD U12*_SD U22*_SD
________ ________ ________ ________ ________
U11*_SD 1.000
U21*_SD 0.376 1.000
U31*_SD 0.030 0.402 1.000
U12*_SD 0.184 -0.024 -0.136 1.000
U22*_SD 0.224 0.095 -0.066 0.497 1.000
U32*_SD 0.220 0.129 0.011 0.325 0.438
U13*_SD 0.068 -0.097 -0.197 0.203 0.223
U23*_SD 0.136 -0.023 -0.104 0.213 0.209
U33*_SD 0.136 -0.070 -0.100 0.243 0.201
F1_SD 0.358 0.426 0.387 0.045 0.114
F2_SD 0.172 0.071 -0.013 0.456 0.524
F3_SD 0.185 -0.029 -0.079 0.229 0.169
I_SD 0.225 0.238 0.120 0.091 0.136
S_SD 0.054 0.105 0.136 0.008 -0.046
Correlations
U32*_SD U13*_SD U23*_SD U33*_SD F1_SD
________ ________ ________ ________ ________
U32*_SD 1.000
U13*_SD 0.136 1.000
U23*_SD 0.205 0.440 1.000
U33*_SD 0.204 0.461 0.464 1.000
F1_SD 0.137 -0.068 0.047 0.071 1.000
F2_SD 0.496 0.130 0.191 0.227 0.152
F3_SD 0.163 0.569 0.561 0.592 0.036
I_SD 0.146 0.030 0.075 0.134 0.435
S_SD 0.050 -0.047 -0.010 -0.016 0.193
Correlations
F2_SD F3_SD I_SD S_SD
________ ________ ________ ________
F2_SD 1.000
F3_SD 0.209 1.000
I_SD 0.245 0.139 1.000
S_SD -0.002 0.001 0.445 1.000
SAVEDATA INFORMATION
Save file
ex11.7imp*.dat
Order of variables
U11
U21
U31
U12
U22
U32
U13
U23
U33
U11*
U21*
U31*
U12*
U22*
U32*
U13*
U23*
U33*
F1
F2
F3
I
S
Save file format Free
Save file record length 10000
Save missing symbol *
Save file
ex11.7plaus.dat
Order and format of variables
U11 F10.3
U21 F10.3
U31 F10.3
U12 F10.3
U22 F10.3
U32 F10.3
U13 F10.3
U23 F10.3
U33 F10.3
U11* Mean F10.3
U11* Median F10.3
U11* Standard Deviation F10.3
U11* 2.5% Value F10.3
U11* 97.5% Value F10.3
U21* Mean F10.3
U21* Median F10.3
U21* Standard Deviation F10.3
U21* 2.5% Value F10.3
U21* 97.5% Value F10.3
U31* Mean F10.3
U31* Median F10.3
U31* Standard Deviation F10.3
U31* 2.5% Value F10.3
U31* 97.5% Value F10.3
U12* Mean F10.3
U12* Median F10.3
U12* Standard Deviation F10.3
U12* 2.5% Value F10.3
U12* 97.5% Value F10.3
U22* Mean F10.3
U22* Median F10.3
U22* Standard Deviation F10.3
U22* 2.5% Value F10.3
U22* 97.5% Value F10.3
U32* Mean F10.3
U32* Median F10.3
U32* Standard Deviation F10.3
U32* 2.5% Value F10.3
U32* 97.5% Value F10.3
U13* Mean F10.3
U13* Median F10.3
U13* Standard Deviation F10.3
U13* 2.5% Value F10.3
U13* 97.5% Value F10.3
U23* Mean F10.3
U23* Median F10.3
U23* Standard Deviation F10.3
U23* 2.5% Value F10.3
U23* 97.5% Value F10.3
U33* Mean F10.3
U33* Median F10.3
U33* Standard Deviation F10.3
U33* 2.5% Value F10.3
U33* 97.5% Value F10.3
F1 Mean F10.3
F1 Median F10.3
F1 Standard Deviation F10.3
F1 2.5% Value F10.3
F1 97.5% Value F10.3
F2 Mean F10.3
F2 Median F10.3
F2 Standard Deviation F10.3
F2 2.5% Value F10.3
F2 97.5% Value F10.3
F3 Mean F10.3
F3 Median F10.3
F3 Standard Deviation F10.3
F3 2.5% Value F10.3
F3 97.5% Value F10.3
I Mean F10.3
I Median F10.3
I Standard Deviation F10.3
I 2.5% Value F10.3
I 97.5% Value F10.3
S Mean F10.3
S Median F10.3
S Standard Deviation F10.3
S 2.5% Value F10.3
S 97.5% Value F10.3
Save file format
79F10.3
Save file record length 10000
Save missing symbol *
Beginning Time: 23:05:16
Ending Time: 23:05:23
Elapsed Time: 00:00:07
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