Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:05 PM
INPUT INSTRUCTIONS
TITLE: this is an example of multiple imputation
using a two-level factor model
with categorical outcomes
DATA: FILE = ex11.8.dat;
VARIABLE: NAMES are u11 u21 u31 u12 u22 u32 u13 u23 u33 clus;
CATEGORICAL = u11-u33;
CLUSTER = clus;
MISSING = ALL (999);
ANALYSIS: TYPE = TWOLEVEL;
ESTIMATOR = BAYES;
PROCESSORS = 2;
MODEL: %WITHIN%
f1w BY u11
u21 (1)
u31 (2);
f2w BY u12
u22 (1)
u32 (2);
f3w BY u13
u23 (1)
u33 (2);
%BETWEEN%
fb BY u11-u33*1;
fb@1;
DATA IMPUTATION:
IMPUTE = u11-u33(c);
SAVE = ex11.8imp*.dat;
OUTPUT: TECH1 TECH8;
*** WARNING
One or more individual-level variables have no variation within a
cluster for the following clusters.
Variable Cluster IDs with no within-cluster variation
U31 8
U12 4 6 7
U22 4 7
U32 7
U13 5 7
U23 5 7 18
U33 7
1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
this is an example of multiple imputation
using a two-level factor model
with categorical outcomes
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 1000
Number of replications
Requested 5
Completed 5
Number of dependent variables 9
Number of independent variables 0
Number of continuous latent variables 4
Observed dependent variables
Binary and ordered categorical (ordinal)
U11 U21 U31 U12 U22 U32
U13 U23 U33
Continuous latent variables
F1W F2W F3W FB
Variables with special functions
Cluster variable CLUS
Variables used for imputation
Variables imputed as categorical
U11 U21 U31 U12 U22 U32
U13 U23 U33
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 5
Iteration intervals for thinning 100
Input data file(s)
ex11.8.dat
Input data format FREE
SUMMARY OF DATA
Number of clusters 20
Size (s) Cluster ID with Size s
50 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
SUMMARY OF MISSING DATA PATTERNS
Number of missing data patterns 63
MISSING DATA PATTERNS (x = not missing)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
U11 x x x x x x x x x x x x x x x x x x x x
U21 x x x x x x x x x x x x x x x x x x x x
U31 x x x x x x x x x x x x x x x x x x x x
U12 x x x x x x x x x x x x x x x
U22 x x x x x x x x x x x x x
U32 x x x x x x x x x x x x x x
U13 x x x x x x x x x x x x x x
U23 x x x x x x x x x x x x x x
U33 x x x x x x x x x x x x x x
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
U11 x x x x x x x x x x x x x x x x x x x x
U21 x x x x x x x x x x x x x x x x x x x x
U31 x x x x x x x x x x x x x x x x x x x x
U12 x x x x x x x x
U22 x x x x x x x x x x x x x
U32 x x x x x x x x x x x
U13 x x x x x x x x x x x
U23 x x x x x x x x x x
U33 x x x x x x x x
41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
U11 x x x x x x x x x x x x x x x x x x x x
U21 x x x x x x x x x x x x x x x x x x x x
U31 x x x x x x x x x x x x x x x x x x x x
U12 x x x x x x x x x
U22 x x x x x
U32 x x x x x x
U13 x x x x x x
U23 x x x x x x x x
U33 x x x x x x x x
61 62 63
U11 x x x
U21 x x x
U31 x x x
U12
U22 x
U32
U13 x
U23
U33 x x
MISSING DATA PATTERN FREQUENCIES
Pattern Frequency Pattern Frequency Pattern Frequency
1 256 22 5 43 3
2 73 23 4 44 5
3 65 24 6 45 4
4 57 25 11 46 3
5 56 26 3 47 1
6 62 27 6 48 2
7 8 28 4 49 1
8 56 29 6 50 1
9 19 30 16 51 2
10 19 31 12 52 4
11 21 32 5 53 2
12 10 33 5 54 1
13 21 34 10 55 1
14 4 35 18 56 1
15 2 36 4 57 1
16 14 37 11 58 1
17 18 38 1 59 1
18 17 39 4 60 2
19 13 40 6 61 1
20 15 41 7 62 1
21 7 42 4 63 1
COVARIANCE COVERAGE OF DATA
Minimum covariance coverage value 0.100
PROPORTION OF DATA PRESENT
Covariance Coverage
U11 U21 U31 U12 U22
________ ________ ________ ________ ________
U11 1.000
U21 1.000 1.000
U31 1.000 1.000 1.000
U12 0.785 0.785 0.785 0.785
U22 0.797 0.797 0.797 0.628 0.797
U32 0.799 0.799 0.799 0.637 0.639
U13 0.783 0.783 0.783 0.626 0.635
U23 0.760 0.760 0.760 0.614 0.608
U33 0.766 0.766 0.766 0.613 0.614
Covariance Coverage
U32 U13 U23 U33
________ ________ ________ ________
U32 0.799
U13 0.631 0.783
U23 0.610 0.607 0.760
U33 0.619 0.594 0.586 0.766
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
U11
Category 1 0.511 511.000
Category 2 0.489 489.000
U21
Category 1 0.460 460.000
Category 2 0.540 540.000
U31
Category 1 0.602 602.000
Category 2 0.398 398.000
U12
Category 1 0.315 247.000
Category 2 0.685 538.000
U22
Category 1 0.228 182.000
Category 2 0.772 615.000
U32
Category 1 0.378 302.000
Category 2 0.622 497.000
U13
Category 1 0.241 189.000
Category 2 0.759 594.000
U23
Category 1 0.167 127.000
Category 2 0.833 633.000
U33
Category 1 0.329 252.000
Category 2 0.671 514.000
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 35
Bayesian Posterior Predictive Checking using Chi-Square
95% Confidence Interval for the Difference Between
the Observed and the Replicated Chi-Square Values
-36.555 46.017
Posterior Predictive P-Value 0.472
MODEL RESULTS
Posterior One-Tailed 95% C.I.
Estimate S.D. P-Value Lower 2.5% Upper 2.5% Significance
Within Level
F1W BY
U11 1.000 0.000 0.000 1.000 1.000
U21 1.192 0.136 0.000 1.006 1.513 *
U31 0.939 0.092 0.000 0.751 1.100 *
F2W BY
U12 1.000 0.000 0.000 1.000 1.000
U22 1.192 0.136 0.000 1.006 1.513 *
U32 0.939 0.092 0.000 0.751 1.100 *
F3W BY
U13 1.000 0.000 0.000 1.000 1.000
U23 1.192 0.136 0.000 1.006 1.513 *
U33 0.939 0.092 0.000 0.751 1.100 *
F2W WITH
F1W 0.795 0.122 0.000 0.594 1.076 *
F3W WITH
F1W 0.750 0.138 0.000 0.525 1.055 *
F2W 1.552 0.232 0.000 1.132 2.035 *
Variances
F1W 1.196 0.201 0.000 0.873 1.651 *
F2W 1.408 0.250 0.000 0.989 1.914 *
F3W 2.752 0.496 0.000 1.817 3.741 *
Between Level
FB BY
U11 0.748 0.335 0.010 0.123 1.457 *
U21 0.819 0.422 0.024 0.002 1.697 *
U31 0.608 0.349 0.031 -0.046 1.357
U12 1.052 0.488 0.009 0.217 2.209 *
U22 1.632 0.594 0.001 0.624 3.004 *
U32 0.614 0.399 0.045 -0.107 1.493
U13 1.287 0.528 0.004 0.386 2.485 *
U23 1.531 0.662 0.004 0.404 2.963 *
U33 1.015 0.465 0.007 0.198 2.083 *
Thresholds
U11$1 0.111 0.260 0.315 -0.403 0.650
U21$1 -0.193 0.344 0.283 -0.854 0.499
U31$1 0.528 0.276 0.026 -0.009 1.112
U12$1 -1.039 0.336 0.003 -1.739 -0.361 *
U22$1 -1.668 0.470 0.001 -2.592 -0.756 *
U32$1 -0.592 0.289 0.021 -1.168 -0.025 *
U13$1 -1.589 0.402 0.000 -2.413 -0.833 *
U23$1 -2.451 0.439 0.000 -3.375 -1.632 *
U33$1 -0.954 0.353 0.006 -1.654 -0.291 *
Variances
FB 1.000 0.000 0.000 1.000 1.000
Residual Variances
U11 0.758 0.436 0.000 0.279 1.991 *
U21 1.411 0.841 0.000 0.605 3.727 *
U31 0.875 0.512 0.000 0.339 2.295 *
U12 1.040 0.748 0.000 0.222 3.174 *
U22 1.497 0.939 0.000 0.554 4.212 *
U32 1.093 0.560 0.000 0.498 2.581 *
U13 1.103 0.714 0.000 0.357 3.129 *
U23 0.805 0.822 0.000 0.090 3.017 *
U33 0.887 0.625 0.000 0.294 2.558 *
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
TAU
U11$1 U21$1 U31$1 U12$1 U22$1
________ ________ ________ ________ ________
0 0 0 0 0
TAU
U32$1 U13$1 U23$1 U33$1
________ ________ ________ ________
0 0 0 0
NU
U11 U21 U31 U12 U22
________ ________ ________ ________ ________
0 0 0 0 0
NU
U32 U13 U23 U33
________ ________ ________ ________
0 0 0 0
LAMBDA
F1W F2W F3W
________ ________ ________
U11 0 0 0
U21 1 0 0
U31 2 0 0
U12 0 0 0
U22 0 1 0
U32 0 2 0
U13 0 0 0
U23 0 0 1
U33 0 0 2
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
F1W F2W F3W
________ ________ ________
0 0 0
BETA
F1W F2W F3W
________ ________ ________
F1W 0 0 0
F2W 0 0 0
F3W 0 0 0
PSI
F1W F2W F3W
________ ________ ________
F1W 3
F2W 4 5
F3W 6 7 8
PARAMETER SPECIFICATION FOR BETWEEN
TAU
U11$1 U21$1 U31$1 U12$1 U22$1
________ ________ ________ ________ ________
27 28 29 30 31
TAU
U32$1 U13$1 U23$1 U33$1
________ ________ ________ ________
32 33 34 35
NU
U11 U21 U31 U12 U22
________ ________ ________ ________ ________
0 0 0 0 0
NU
U32 U13 U23 U33
________ ________ ________ ________
0 0 0 0
LAMBDA
FB
________
U11 9
U21 10
U31 11
U12 12
U22 13
U32 14
U13 15
U23 16
U33 17
THETA
U11 U21 U31 U12 U22
________ ________ ________ ________ ________
U11 18
U21 0 19
U31 0 0 20
U12 0 0 0 21
U22 0 0 0 0 22
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 23
U13 0 24
U23 0 0 25
U33 0 0 0 26
ALPHA
FB
________
0
BETA
FB
________
FB 0
PSI
FB
________
FB 0
STARTING VALUES FOR WITHIN
TAU
U11$1 U21$1 U31$1 U12$1 U22$1
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
TAU
U32$1 U13$1 U23$1 U33$1
________ ________ ________ ________
0.000 0.000 0.000 0.000
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
F1W F2W F3W
________ ________ ________
U11 1.000 0.000 0.000
U21 1.000 0.000 0.000
U31 1.000 0.000 0.000
U12 0.000 1.000 0.000
U22 0.000 1.000 0.000
U32 0.000 1.000 0.000
U13 0.000 0.000 1.000
U23 0.000 0.000 1.000
U33 0.000 0.000 1.000
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
F1W F2W F3W
________ ________ ________
0.000 0.000 0.000
BETA
F1W F2W F3W
________ ________ ________
F1W 0.000 0.000 0.000
F2W 0.000 0.000 0.000
F3W 0.000 0.000 0.000
PSI
F1W F2W F3W
________ ________ ________
F1W 1.000
F2W 0.000 1.000
F3W 0.000 0.000 1.000
STARTING VALUES FOR BETWEEN
TAU
U11$1 U21$1 U31$1 U12$1 U22$1
________ ________ ________ ________ ________
0.024 -0.089 0.230 -0.432 -0.676
TAU
U32$1 U13$1 U23$1 U33$1
________ ________ ________ ________
-0.277 -0.636 -0.892 -0.396
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
FB
________
U11 1.000
U21 1.000
U31 1.000
U12 1.000
U22 1.000
U32 1.000
U13 1.000
U23 1.000
U33 1.000
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
FB
________
0.000
BETA
FB
________
FB 0.000
PSI
FB
________
FB 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~IW(1.000,4) infinity infinity infinity
Parameter 4~IW(0.000,4) infinity infinity infinity
Parameter 5~IW(1.000,4) infinity infinity infinity
Parameter 6~IW(0.000,4) infinity infinity infinity
Parameter 7~IW(0.000,4) infinity infinity infinity
Parameter 8~IW(1.000,4) infinity infinity infinity
Parameter 9~N(0.000,5.000) 0.0000 5.0000 2.2361
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
Parameter 13~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 14~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 15~N(0.000,5.000) 0.0000 5.0000 2.2361
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~IG(-1.000,0.000) infinity infinity infinity
Parameter 19~IG(-1.000,0.000) infinity infinity infinity
Parameter 20~IG(-1.000,0.000) infinity infinity infinity
Parameter 21~IG(-1.000,0.000) infinity infinity infinity
Parameter 22~IG(-1.000,0.000) infinity infinity infinity
Parameter 23~IG(-1.000,0.000) infinity infinity infinity
Parameter 24~IG(-1.000,0.000) infinity infinity infinity
Parameter 25~IG(-1.000,0.000) infinity infinity infinity
Parameter 26~IG(-1.000,0.000) infinity infinity infinity
Parameter 27~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 28~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 29~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 30~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 31~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 32~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 33~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 34~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 35~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 2.893 2
200 4.232 1
300 4.516 2
400 3.436 3
500 3.099 3
600 2.959 1
700 3.501 1
800 2.425 8
900 2.959 8
1000 3.395 8
1100 2.957 8
1200 2.026 2
1300 1.719 2
1400 1.355 2
1500 1.351 2
1600 1.296 2
1700 1.296 2
1800 1.282 1
1900 1.299 1
2000 1.289 1
2100 1.327 1
2200 1.347 1
2300 1.327 1
2400 1.291 1
2500 1.289 1
2600 1.289 1
2700 1.146 1
2800 1.048 8
SAVEDATA INFORMATION
Save file
ex11.8imp*.dat
Order of variables
U11
U21
U31
U12
U22
U32
U13
U23
U33
CLUS
Save file format Free
Save file record length 10000
Save missing symbol *
Beginning Time: 23:05:23
Ending Time: 23:05:28
Elapsed Time: 00:00:05
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