Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:04 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a linear growth model
with missing data on a continuous outcome
using a missing data correlate to improve
the plausibility of MAR
DATA: FILE = ex11.1.dat;
VARIABLE: NAMES = x1 y1-y4 z x2;
USEVARIABLES = y1-y4;
MISSING = ALL (999);
AUXILIARY = (m) z;
ANALYSIS: ESTIMATOR = ML;
MODEL: i s | y1@0 y2@1 y3@2 y4@3;
OUTPUT: TECH1;
INPUT READING TERMINATED NORMALLY
this is an example of a linear growth model
with missing data on a continuous outcome
using a missing data correlate to improve
the plausibility of MAR
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 200
Number of dependent variables 4
Number of independent variables 0
Number of continuous latent variables 2
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4
Observed auxiliary variables
Z
Continuous latent variables
I S
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
Input data file(s)
ex11.1.dat
Input data format FREE
SUMMARY OF DATA
Number of missing data patterns 15
COVARIANCE COVERAGE OF DATA
Minimum covariance coverage value 0.100
PROPORTION OF DATA PRESENT
Covariance Coverage
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 0.710
Y2 0.425 0.615
Y3 0.390 0.355 0.525
Y4 0.330 0.320 0.280 0.420
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
Z 0.016 0.144 -2.954 0.50% -0.817 -0.264 -0.055
200.000 0.934 0.060 2.787 0.50% 0.236 0.830
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 9
Loglikelihood Including the Auxiliary Part
H0 Value -1009.197
H1 Value -1007.232
Information Criteria Including the Auxiliary Part
Number of Free Parameters 15
Akaike (AIC) 2048.394
Bayesian (BIC) 2097.869
Sample-Size Adjusted BIC 2050.347
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit
Value 3.930
Degrees of Freedom 5
P-Value 0.5595
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.000
90 Percent C.I. 0.000 0.087
Probability RMSEA <= .05 0.776
CFI/TLI
CFI 1.000
TLI 1.000
Chi-Square Test of Model Fit for the Baseline Model
Value 276.533
Degrees of Freedom 6
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value 0.047
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
I |
Y1 1.000 0.000 999.000 999.000
Y2 1.000 0.000 999.000 999.000
Y3 1.000 0.000 999.000 999.000
Y4 1.000 0.000 999.000 999.000
S |
Y1 0.000 0.000 999.000 999.000
Y2 1.000 0.000 999.000 999.000
Y3 2.000 0.000 999.000 999.000
Y4 3.000 0.000 999.000 999.000
S WITH
I 0.226 0.083 2.707 0.007
Means
I 1.417 0.096 14.717 0.000
S 2.011 0.057 35.557 0.000
Intercepts
Y1 0.000 0.000 999.000 999.000
Y2 0.000 0.000 999.000 999.000
Y3 0.000 0.000 999.000 999.000
Y4 0.000 0.000 999.000 999.000
Variances
I 1.101 0.195 5.634 0.000
S 0.261 0.058 4.513 0.000
Residual Variances
Y1 0.616 0.153 4.023 0.000
Y2 0.441 0.094 4.706 0.000
Y3 0.531 0.130 4.089 0.000
Y4 0.257 0.203 1.261 0.207
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.824E-02
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION
NU
Y1 Y2 Y3 Y4
________ ________ ________ ________
0 0 0 0
LAMBDA
I S
________ ________
Y1 0 0
Y2 0 0
Y3 0 0
Y4 0 0
THETA
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 1
Y2 0 2
Y3 0 0 3
Y4 0 0 0 4
ALPHA
I S
________ ________
5 6
BETA
I S
________ ________
I 0 0
S 0 0
PSI
I S
________ ________
I 7
S 8 9
STARTING VALUES
NU
Y1 Y2 Y3 Y4
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
I S
________ ________
Y1 1.000 0.000
Y2 1.000 1.000
Y3 1.000 2.000
Y4 1.000 3.000
THETA
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 0.616
Y2 0.000 0.441
Y3 0.000 0.000 0.531
Y4 0.000 0.000 0.000 0.257
ALPHA
I S
________ ________
1.417 2.011
BETA
I S
________ ________
I 0.000 0.000
S 0.000 0.000
PSI
I S
________ ________
I 1.101
S 0.226 0.261
Beginning Time: 23:04:54
Ending Time: 23:04:54
Elapsed Time: 00:00:00
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