Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:05 PM
INPUT INSTRUCTIONS
TITLE: this is an example of multiple imputation
for a set of variables with missing values
followed by a growth model analysis by
maximum-likelihood estimation
DATA: FILE = ex11.6.dat;
VARIABLE: NAMES = x1 y1-y4 z x2;
USEVARIABLES = y1-y4 x1 x2;
MISSING = ALL(999);
DATA IMPUTATION:
IMPUTE = y1-y4 x1 (c) x2;
NDATASETS = 10;
ANALYSIS: ESTIMATOR = ML;
MODEL: i s | y1@0 y2@1 y3@2 y4@3;
i s ON x1 x2;
OUTPUT: TECH1;
*** WARNING
Data set contains cases with missing on all variables except
x-variables. These cases were not included in the analysis.
Number of cases with missing on all variables except x-variables: 13
1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
this is an example of multiple imputation
for a set of variables with missing values
followed by a growth model analysis by
maximum-likelihood estimation
SUMMARY OF ANALYSIS
Number of groups 1
Average number of observations 187
Number of replications
Requested 10
Completed 10
Number of dependent variables 4
Number of independent variables 2
Number of continuous latent variables 2
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4
Observed independent variables
X1 X2
Continuous latent variables
I S
Variables used for imputation
Variables imputed as continuous
Y1 Y2 Y3 Y4 X2
Variables imputed as categorical
X1
Estimator ML
Information matrix OBSERVED
Maximum number of iterations 1000
Convergence criterion 0.500D-04
Maximum number of steepest descent iterations 20
Maximum number of iterations for H1 2000
Convergence criterion for H1 0.100D-03
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
Specifications for Data Imputation
Number of imputed data sets 10
H1 imputation model type COVARIANCE
Iteration intervals for thinning 100
Input data file(s)
ex11.6.dat
Input data format FREE
SUMMARY OF DATA FOR THE FIRST DATA SET
Number of missing data patterns 1
SUMMARY OF MISSING DATA PATTERNS FOR THE FIRST DATA SET
MISSING DATA PATTERNS (x = not missing)
1
Y1 x
Y2 x
Y3 x
Y4 x
X1 x
X2 x
MISSING DATA PATTERN FREQUENCIES
Pattern Frequency
1 187
COVARIANCE COVERAGE OF DATA FOR THE FIRST DATA SET
Minimum covariance coverage value 0.100
PROPORTION OF DATA PRESENT
Covariance Coverage
Y1 Y2 Y3 Y4 X1
________ ________ ________ ________ ________
Y1 1.000
Y2 1.000 1.000
Y3 1.000 1.000 1.000
Y4 1.000 1.000 1.000 1.000
X1 1.000 1.000 1.000 1.000 1.000
X2 1.000 1.000 1.000 1.000 1.000
Covariance Coverage
X2
________
X2 1.000
SAMPLE STATISTICS
NOTE: These are average results over 10 data sets.
SAMPLE STATISTICS
Means
Y1 Y2 Y3 Y4 X1
________ ________ ________ ________ ________
1.401 3.454 5.562 7.539 0.446
Means
X2
________
-0.142
Covariances
Y1 Y2 Y3 Y4 X1
________ ________ ________ ________ ________
Y1 1.718
Y2 1.315 2.237
Y3 1.636 2.460 3.935
Y4 1.825 2.734 4.023 5.198
X1 0.246 0.306 0.389 0.382 0.247
X2 0.438 0.532 0.791 1.131 0.000
Covariances
X2
________
X2 1.094
Correlations
Y1 Y2 Y3 Y4 X1
________ ________ ________ ________ ________
Y1 1.000
Y2 0.671 1.000
Y3 0.629 0.829 1.000
Y4 0.611 0.802 0.890 1.000
X1 0.378 0.412 0.395 0.337 1.000
X2 0.319 0.340 0.381 0.474 0.001
Correlations
X2
________
X2 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
Y1 1.325 -0.033 -1.656 0.70% 0.111 0.957 1.344
142.000 1.786 -0.667 4.410 0.70% 1.729 2.583
Y2 3.370 -0.245 -0.896 0.81% 1.921 3.091 3.467
123.000 2.188 -0.179 6.951 0.81% 3.911 4.538
Y3 5.152 -0.170 0.890 0.95% 3.222 4.799 5.277
105.000 3.906 -0.527 9.372 0.95% 5.683 6.809
Y4 6.578 0.012 0.836 1.19% 4.750 5.886 6.361
84.000 4.786 -0.447 11.389 1.19% 6.873 8.728
X1 0.455 0.183 0.000 54.55% 0.000 0.000 0.000
154.000 0.248 -1.967 1.000 45.45% 1.000 1.000
X2 -0.136 0.260 -2.762 0.67% -0.973 -0.448 -0.215
149.000 1.101 0.224 2.786 0.67% 0.028 0.660
MODEL FIT INFORMATION
Number of Free Parameters 13
Loglikelihood
H0 Value -1102.804
H1 Value -1085.163
* The loglikelihood cannot be used directly for chi-square testing with
imputed data.
Information Criteria
Akaike (AIC) 2231.607
Bayesian (BIC) 2273.612
Sample-Size Adjusted BIC 2232.435
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit
Value 4.392
Degrees of Freedom 9
P-Value 0.8838
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.000
90 Percent C.I. 0.000 0.040
Probability RMSEA <= .05 0.970
CFI/TLI
CFI 1.000
TLI 1.000
Chi-Square Test of Model Fit for the Baseline Model
Value 200.582
Degrees of Freedom 14
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value 0.031
MODEL RESULTS
Two-Tailed Rate of
Estimate S.E. Est./S.E. P-Value Missing
I |
Y1 1.000 0.000 999.000 999.000 0.000
Y2 1.000 0.000 999.000 999.000 0.000
Y3 1.000 0.000 999.000 999.000 0.000
Y4 1.000 0.000 999.000 999.000 0.000
S |
Y1 0.000 0.000 999.000 999.000 0.000
Y2 1.000 0.000 999.000 999.000 0.000
Y3 2.000 0.000 999.000 999.000 0.000
Y4 3.000 0.000 999.000 999.000 0.000
I ON
X1 1.053 0.196 5.358 0.000 0.393
X2 0.323 0.086 3.749 0.000 0.265
S ON
X1 0.189 0.112 1.683 0.092 0.512
X2 0.224 0.073 3.087 0.002 0.747
S WITH
I 0.115 0.091 1.262 0.207 0.751
Intercepts
Y1 0.000 0.000 999.000 999.000 0.000
Y2 0.000 0.000 999.000 999.000 0.000
Y3 0.000 0.000 999.000 999.000 0.000
Y4 0.000 0.000 999.000 999.000 0.000
I 0.991 0.144 6.894 0.000 0.500
S 1.993 0.077 25.736 0.000 0.549
Residual Variances
Y1 0.655 0.186 3.524 0.000 0.692
Y2 0.456 0.085 5.361 0.000 0.446
Y3 0.554 0.137 4.033 0.000 0.664
Y4 0.340 0.254 1.337 0.181 0.776
I 0.707 0.193 3.667 0.000 0.631
S 0.199 0.061 3.284 0.001 0.709
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.307E-01
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION
NU
Y1 Y2 Y3 Y4 X1
________ ________ ________ ________ ________
0 0 0 0 0
NU
X2
________
0
LAMBDA
I S X1 X2
________ ________ ________ ________
Y1 0 0 0 0
Y2 0 0 0 0
Y3 0 0 0 0
Y4 0 0 0 0
X1 0 0 0 0
X2 0 0 0 0
THETA
Y1 Y2 Y3 Y4 X1
________ ________ ________ ________ ________
Y1 1
Y2 0 2
Y3 0 0 3
Y4 0 0 0 4
X1 0 0 0 0 0
X2 0 0 0 0 0
THETA
X2
________
X2 0
ALPHA
I S X1 X2
________ ________ ________ ________
5 6 0 0
BETA
I S X1 X2
________ ________ ________ ________
I 0 0 7 8
S 0 0 9 10
X1 0 0 0 0
X2 0 0 0 0
PSI
I S X1 X2
________ ________ ________ ________
I 11
S 12 13
X1 0 0 0
X2 0 0 0 0
STARTING VALUES
NU
Y1 Y2 Y3 Y4 X1
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
X2
________
0.000
LAMBDA
I S X1 X2
________ ________ ________ ________
Y1 1.000 0.000 0.000 0.000
Y2 1.000 1.000 0.000 0.000
Y3 1.000 2.000 0.000 0.000
Y4 1.000 3.000 0.000 0.000
X1 0.000 0.000 1.000 0.000
X2 0.000 0.000 0.000 1.000
THETA
Y1 Y2 Y3 Y4 X1
________ ________ ________ ________ ________
Y1 0.893
Y2 0.000 1.094
Y3 0.000 0.000 1.953
Y4 0.000 0.000 0.000 2.393
X1 0.000 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000 0.000
THETA
X2
________
X2 0.000
ALPHA
I S X1 X2
________ ________ ________ ________
1.303 1.991 0.444 -0.131
BETA
I S X1 X2
________ ________ ________ ________
I 0.000 0.000 0.000 0.000
S 0.000 0.000 0.000 0.000
X1 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000
PSI
I S X1 X2
________ ________ ________ ________
I 1.557
S 0.000 0.633
X1 0.000 0.000 0.247
X2 0.000 0.000 0.016 1.069
Beginning Time: 23:05:16
Ending Time: 23:05:16
Elapsed Time: 00:00:00
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