Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:04 PM
INPUT INSTRUCTIONS
TITLE: this is an example of modeling with data
not missing at random (NMAR) using the
Diggle-Kenward selection model
DATA: FILE = ex11.3.dat;
VARIABLE: NAMES = z1-z5 y0 y1-y5;
USEVARIABLES = y0-y5 d1-d5;
MISSING = ALL (999);
CATEGORICAL = d1-d5;
DATA MISSING:
NAMES = y0-y5;
TYPE = SDROPOUT;
BINARY = d1-d5;
ANALYSIS: ESTIMATOR = ML;
ALGORITHM = INTEGRATION;
INTEGRATION = MONTECARLO;
PROCESSORS = 2;
MODEL: i s | y0@0 y1@1 y2@2 y3@3 y4@4 y5@5;
d1 ON y0 (1)
y1 (2);
d2 ON y1 (1)
y2 (2);
d3 ON y2 (1)
y3 (2);
d4 ON y3 (1)
y4 (2);
d5 ON y4 (1)
y5 (2);
OUTPUT: TECH1;
INPUT READING TERMINATED NORMALLY
this is an example of modeling with data
not missing at random (NMAR) using the
Diggle-Kenward selection model
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 1000
Number of dependent variables 11
Number of independent variables 0
Number of continuous latent variables 2
Observed dependent variables
Continuous
Y0 Y1 Y2 Y3 Y4 Y5
Binary and ordered categorical (ordinal)
D1 D2 D3 D4 D5
Continuous latent variables
I S
Estimator ML
Information matrix OBSERVED
Optimization Specifications for the Quasi-Newton Algorithm for
Continuous Outcomes
Maximum number of iterations 100
Convergence criterion 0.100D-05
Optimization Specifications for the EM Algorithm
Maximum number of iterations 500
Convergence criteria
Loglikelihood change 0.100D-02
Relative loglikelihood change 0.100D-05
Derivative 0.100D-02
Optimization Specifications for the M step of the EM Algorithm for
Categorical Latent variables
Number of M step iterations 1
M step convergence criterion 0.100D-02
Basis for M step termination ITERATION
Optimization Specifications for the M step of the EM Algorithm for
Censored, Binary or Ordered Categorical (Ordinal), Unordered
Categorical (Nominal) and Count Outcomes
Number of M step iterations 1
M step convergence criterion 0.100D-02
Basis for M step termination ITERATION
Maximum value for logit thresholds 15
Minimum value for logit thresholds -15
Minimum expected cell size for chi-square 0.100D-01
Maximum number of iterations for H1 2000
Convergence criterion for H1 0.100D-03
Optimization algorithm EMA
Integration Specifications
Type MONTECARLO
Number of integration points 1250
Dimensions of numerical integration 5
Adaptive quadrature ON
Monte Carlo integration seed 0
Link LOGIT
Cholesky OFF
Input data file(s)
ex11.3.dat
Input data format FREE
SUMMARY OF DATA
Number of missing data patterns 32
Number of y missing data patterns 32
Number of u missing data patterns 5
COVARIANCE COVERAGE OF DATA
Minimum covariance coverage value 0.100
PROPORTION OF DATA PRESENT
Covariance Coverage
D1 D2 D3 D4 D5
________ ________ ________ ________ ________
D1 1.000
D2 0.967 0.967
D3 0.932 0.932 0.932
D4 0.878 0.878 0.878 0.878
D5 0.838 0.838 0.838 0.838 0.838
Y0 1.000 0.967 0.932 0.878 0.838
Y1 0.736 0.736 0.701 0.671 0.645
Y2 0.693 0.693 0.693 0.639 0.621
Y3 0.615 0.615 0.615 0.615 0.575
Y4 0.724 0.724 0.724 0.724 0.724
Y5 0.687 0.687 0.687 0.687 0.687
Covariance Coverage
Y0 Y1 Y2 Y3 Y4
________ ________ ________ ________ ________
Y0 1.000
Y1 0.736 0.736
Y2 0.693 0.535 0.693
Y3 0.615 0.491 0.469 0.615
Y4 0.724 0.562 0.555 0.516 0.724
Y5 0.687 0.541 0.530 0.501 0.573
Covariance Coverage
Y5
________
Y5 0.687
PROPORTION OF DATA PRESENT FOR U
Covariance Coverage
D1 D2 D3 D4 D5
________ ________ ________ ________ ________
D1 1.000
D2 0.967 0.967
D3 0.932 0.932 0.932
D4 0.878 0.878 0.878 0.878
D5 0.838 0.838 0.838 0.838 0.838
PROPORTION OF DATA PRESENT FOR Y
Covariance Coverage
Y0 Y1 Y2 Y3 Y4
________ ________ ________ ________ ________
Y0 1.000
Y1 0.736 0.736
Y2 0.693 0.535 0.693
Y3 0.615 0.491 0.469 0.615
Y4 0.724 0.562 0.555 0.516 0.724
Y5 0.687 0.541 0.530 0.501 0.573
Covariance Coverage
Y5
________
Y5 0.687
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
D1
Category 1 0.967 967.000
Category 2 0.033 33.000
D2
Category 1 0.964 932.000
Category 2 0.036 35.000
D3
Category 1 0.942 878.000
Category 2 0.058 54.000
D4
Category 1 0.954 838.000
Category 2 0.046 40.000
D5
Category 1 0.820 687.000
Category 2 0.180 151.000
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
Y0 2.038 0.067 -0.371 0.10% 1.306 1.816 2.017
1000.000 0.692 -0.158 4.779 0.10% 2.256 2.736
Y1 0.900 -0.067 -1.759 0.14% 0.238 0.717 0.914
736.000 0.648 0.094 3.132 0.14% 1.083 1.553
Y2 -0.224 -0.076 -3.059 0.14% -1.061 -0.443 -0.234
693.000 0.969 0.081 2.838 0.14% 0.006 0.617
Y3 -1.437 -0.149 -4.833 0.16% -2.293 -1.670 -1.428
615.000 1.168 -0.008 1.487 0.16% -1.133 -0.508
Y4 -2.476 -0.154 -6.979 0.14% -3.566 -2.734 -2.424
724.000 1.969 0.430 3.148 0.14% -2.142 -1.315
Y5 -3.685 -0.222 -9.753 0.15% -4.903 -4.009 -3.650
687.000 2.383 0.737 0.907 0.15% -3.285 -2.465
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 18
Loglikelihood
H0 Value -6526.797
Information Criteria
Akaike (AIC) 13089.595
Bayesian (BIC) 13177.934
Sample-Size Adjusted BIC 13120.765
(n* = (n + 2) / 24)
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
I |
Y0 1.000 0.000 999.000 999.000
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
Y5 1.000 0.000 999.000 999.000
S |
Y0 0.000 0.000 999.000 999.000
Y1 1.000 0.000 999.000 999.000
Y2 2.000 0.000 999.000 999.000
Y3 3.000 0.000 999.000 999.000
Y4 4.000 0.000 999.000 999.000
Y5 5.000 0.000 999.000 999.000
D1 ON
Y0 0.359 0.160 2.239 0.025
Y1 0.586 0.179 3.265 0.001
D2 ON
Y1 0.359 0.160 2.239 0.025
Y2 0.586 0.179 3.265 0.001
D3 ON
Y2 0.359 0.160 2.239 0.025
Y3 0.586 0.179 3.265 0.001
D4 ON
Y3 0.359 0.160 2.239 0.025
Y4 0.586 0.179 3.265 0.001
D5 ON
Y4 0.359 0.160 2.239 0.025
Y5 0.586 0.179 3.265 0.001
S WITH
I 0.000 0.009 0.030 0.976
Means
I 1.998 0.023 88.323 0.000
S -1.045 0.013 -77.985 0.000
Intercepts
Y0 0.000 0.000 999.000 999.000
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
Y5 0.000 0.000 999.000 999.000
Thresholds
D1$1 4.848 0.260 18.621 0.000
D2$1 3.803 0.221 17.196 0.000
D3$1 2.410 0.192 12.555 0.000
D4$1 1.790 0.214 8.345 0.000
D5$1 -0.842 0.240 -3.503 0.000
Variances
I 0.235 0.025 9.575 0.000
S 0.090 0.006 14.249 0.000
Residual Variances
Y0 0.462 0.030 15.322 0.000
Y1 0.353 0.023 15.107 0.000
Y2 0.333 0.022 14.849 0.000
Y3 0.255 0.021 12.017 0.000
Y4 0.454 0.035 12.840 0.000
Y5 0.435 0.046 9.412 0.000
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.218E-03
(ratio of smallest to largest eigenvalue)
LOGISTIC REGRESSION ODDS RATIO RESULTS
95% C.I.
Estimate S.E. Lower 2.5% Upper 2.5%
D1 ON
Y0 1.432 0.230 1.046 1.962
Y1 1.796 0.322 1.264 2.553
D2 ON
Y1 1.432 0.230 1.046 1.962
Y2 1.796 0.322 1.264 2.553
D3 ON
Y2 1.432 0.230 1.046 1.962
Y3 1.796 0.322 1.264 2.553
D4 ON
Y3 1.432 0.230 1.046 1.962
Y4 1.796 0.322 1.264 2.553
D5 ON
Y4 1.432 0.230 1.046 1.962
Y5 1.796 0.322 1.264 2.553
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION
TAU
D1$1 D2$1 D3$1 D4$1 D5$1
________ ________ ________ ________ ________
14 15 16 17 18
NU
D1 D2 D3 D4 D5
________ ________ ________ ________ ________
0 0 0 0 0
NU
Y0 Y1 Y2 Y3 Y4
________ ________ ________ ________ ________
0 0 0 0 0
NU
Y5
________
0
LAMBDA
I S D1 D2 D3
________ ________ ________ ________ ________
D1 0 0 0 0 0
D2 0 0 0 0 0
D3 0 0 0 0 0
D4 0 0 0 0 0
D5 0 0 0 0 0
Y0 0 0 0 0 0
Y1 0 0 0 0 0
Y2 0 0 0 0 0
Y3 0 0 0 0 0
Y4 0 0 0 0 0
Y5 0 0 0 0 0
LAMBDA
D4 D5 Y0 Y1 Y2
________ ________ ________ ________ ________
D1 0 0 0 0 0
D2 0 0 0 0 0
D3 0 0 0 0 0
D4 0 0 0 0 0
D5 0 0 0 0 0
Y0 0 0 0 0 0
Y1 0 0 0 0 0
Y2 0 0 0 0 0
Y3 0 0 0 0 0
Y4 0 0 0 0 0
Y5 0 0 0 0 0
LAMBDA
Y3 Y4 Y5
________ ________ ________
D1 0 0 0
D2 0 0 0
D3 0 0 0
D4 0 0 0
D5 0 0 0
Y0 0 0 0
Y1 0 0 0
Y2 0 0 0
Y3 0 0 0
Y4 0 0 0
Y5 0 0 0
THETA
D1 D2 D3 D4 D5
________ ________ ________ ________ ________
D1 0
D2 0 0
D3 0 0 0
D4 0 0 0 0
D5 0 0 0 0 0
Y0 0 0 0 0 0
Y1 0 0 0 0 0
Y2 0 0 0 0 0
Y3 0 0 0 0 0
Y4 0 0 0 0 0
Y5 0 0 0 0 0
THETA
Y0 Y1 Y2 Y3 Y4
________ ________ ________ ________ ________
Y0 0
Y1 0 0
Y2 0 0 0
Y3 0 0 0 0
Y4 0 0 0 0 0
Y5 0 0 0 0 0
THETA
Y5
________
Y5 0
ALPHA
I S D1 D2 D3
________ ________ ________ ________ ________
1 2 0 0 0
ALPHA
D4 D5 Y0 Y1 Y2
________ ________ ________ ________ ________
0 0 0 0 0
ALPHA
Y3 Y4 Y5
________ ________ ________
0 0 0
BETA
I S D1 D2 D3
________ ________ ________ ________ ________
I 0 0 0 0 0
S 0 0 0 0 0
D1 0 0 0 0 0
D2 0 0 0 0 0
D3 0 0 0 0 0
D4 0 0 0 0 0
D5 0 0 0 0 0
Y0 0 0 0 0 0
Y1 0 0 0 0 0
Y2 0 0 0 0 0
Y3 0 0 0 0 0
Y4 0 0 0 0 0
Y5 0 0 0 0 0
BETA
D4 D5 Y0 Y1 Y2
________ ________ ________ ________ ________
I 0 0 0 0 0
S 0 0 0 0 0
D1 0 0 3 4 0
D2 0 0 0 3 4
D3 0 0 0 0 3
D4 0 0 0 0 0
D5 0 0 0 0 0
Y0 0 0 0 0 0
Y1 0 0 0 0 0
Y2 0 0 0 0 0
Y3 0 0 0 0 0
Y4 0 0 0 0 0
Y5 0 0 0 0 0
BETA
Y3 Y4 Y5
________ ________ ________
I 0 0 0
S 0 0 0
D1 0 0 0
D2 0 0 0
D3 4 0 0
D4 3 4 0
D5 0 3 4
Y0 0 0 0
Y1 0 0 0
Y2 0 0 0
Y3 0 0 0
Y4 0 0 0
Y5 0 0 0
PSI
I S D1 D2 D3
________ ________ ________ ________ ________
I 5
S 6 7
D1 0 0 0
D2 0 0 0 0
D3 0 0 0 0 0
D4 0 0 0 0 0
D5 0 0 0 0 0
Y0 0 0 0 0 0
Y1 0 0 0 0 0
Y2 0 0 0 0 0
Y3 0 0 0 0 0
Y4 0 0 0 0 0
Y5 0 0 0 0 0
PSI
D4 D5 Y0 Y1 Y2
________ ________ ________ ________ ________
D4 0
D5 0 0
Y0 0 0 8
Y1 0 0 0 9
Y2 0 0 0 0 10
Y3 0 0 0 0 0
Y4 0 0 0 0 0
Y5 0 0 0 0 0
PSI
Y3 Y4 Y5
________ ________ ________
Y3 11
Y4 0 12
Y5 0 0 13
STARTING VALUES
TAU
D1$1 D2$1 D3$1 D4$1 D5$1
________ ________ ________ ________ ________
3.378 3.282 2.789 3.042 1.515
NU
D1 D2 D3 D4 D5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
Y0 Y1 Y2 Y3 Y4
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
Y5
________
0.000
LAMBDA
I S D1 D2 D3
________ ________ ________ ________ ________
D1 0.000 0.000 1.000 0.000 0.000
D2 0.000 0.000 0.000 1.000 0.000
D3 0.000 0.000 0.000 0.000 1.000
D4 0.000 0.000 0.000 0.000 0.000
D5 0.000 0.000 0.000 0.000 0.000
Y0 0.000 0.000 0.000 0.000 0.000
Y1 0.000 0.000 0.000 0.000 0.000
Y2 0.000 0.000 0.000 0.000 0.000
Y3 0.000 0.000 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000 0.000
Y5 0.000 0.000 0.000 0.000 0.000
LAMBDA
D4 D5 Y0 Y1 Y2
________ ________ ________ ________ ________
D1 0.000 0.000 0.000 0.000 0.000
D2 0.000 0.000 0.000 0.000 0.000
D3 0.000 0.000 0.000 0.000 0.000
D4 1.000 0.000 0.000 0.000 0.000
D5 0.000 1.000 0.000 0.000 0.000
Y0 0.000 0.000 1.000 0.000 0.000
Y1 0.000 0.000 0.000 1.000 0.000
Y2 0.000 0.000 0.000 0.000 1.000
Y3 0.000 0.000 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000 0.000
Y5 0.000 0.000 0.000 0.000 0.000
LAMBDA
Y3 Y4 Y5
________ ________ ________
D1 0.000 0.000 0.000
D2 0.000 0.000 0.000
D3 0.000 0.000 0.000
D4 0.000 0.000 0.000
D5 0.000 0.000 0.000
Y0 0.000 0.000 0.000
Y1 0.000 0.000 0.000
Y2 0.000 0.000 0.000
Y3 1.000 0.000 0.000
Y4 0.000 1.000 0.000
Y5 0.000 0.000 1.000
THETA
D1 D2 D3 D4 D5
________ ________ ________ ________ ________
D1 0.000
D2 0.000 0.000
D3 0.000 0.000 0.000
D4 0.000 0.000 0.000 0.000
D5 0.000 0.000 0.000 0.000 0.000
Y0 0.000 0.000 0.000 0.000 0.000
Y1 0.000 0.000 0.000 0.000 0.000
Y2 0.000 0.000 0.000 0.000 0.000
Y3 0.000 0.000 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000 0.000
Y5 0.000 0.000 0.000 0.000 0.000
THETA
Y0 Y1 Y2 Y3 Y4
________ ________ ________ ________ ________
Y0 0.000
Y1 0.000 0.000
Y2 0.000 0.000 0.000
Y3 0.000 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000 0.000
Y5 0.000 0.000 0.000 0.000 0.000
THETA
Y5
________
Y5 0.000
ALPHA
I S D1 D2 D3
________ ________ ________ ________ ________
2.084 -0.942 0.000 0.000 0.000
ALPHA
D4 D5 Y0 Y1 Y2
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
ALPHA
Y3 Y4 Y5
________ ________ ________
0.000 0.000 0.000
BETA
I S D1 D2 D3
________ ________ ________ ________ ________
I 0.000 0.000 0.000 0.000 0.000
S 0.000 0.000 0.000 0.000 0.000
D1 0.000 0.000 0.000 0.000 0.000
D2 0.000 0.000 0.000 0.000 0.000
D3 0.000 0.000 0.000 0.000 0.000
D4 0.000 0.000 0.000 0.000 0.000
D5 0.000 0.000 0.000 0.000 0.000
Y0 1.000 0.000 0.000 0.000 0.000
Y1 1.000 1.000 0.000 0.000 0.000
Y2 1.000 2.000 0.000 0.000 0.000
Y3 1.000 3.000 0.000 0.000 0.000
Y4 1.000 4.000 0.000 0.000 0.000
Y5 1.000 5.000 0.000 0.000 0.000
BETA
D4 D5 Y0 Y1 Y2
________ ________ ________ ________ ________
I 0.000 0.000 0.000 0.000 0.000
S 0.000 0.000 0.000 0.000 0.000
D1 0.000 0.000 0.000 0.000 0.000
D2 0.000 0.000 0.000 0.000 0.000
D3 0.000 0.000 0.000 0.000 0.000
D4 0.000 0.000 0.000 0.000 0.000
D5 0.000 0.000 0.000 0.000 0.000
Y0 0.000 0.000 0.000 0.000 0.000
Y1 0.000 0.000 0.000 0.000 0.000
Y2 0.000 0.000 0.000 0.000 0.000
Y3 0.000 0.000 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000 0.000
Y5 0.000 0.000 0.000 0.000 0.000
BETA
Y3 Y4 Y5
________ ________ ________
I 0.000 0.000 0.000
S 0.000 0.000 0.000
D1 0.000 0.000 0.000
D2 0.000 0.000 0.000
D3 0.000 0.000 0.000
D4 0.000 0.000 0.000
D5 0.000 0.000 0.000
Y0 0.000 0.000 0.000
Y1 0.000 0.000 0.000
Y2 0.000 0.000 0.000
Y3 0.000 0.000 0.000
Y4 0.000 0.000 0.000
Y5 0.000 0.000 0.000
PSI
I S D1 D2 D3
________ ________ ________ ________ ________
I 0.530
S 0.000 0.232
D1 0.000 0.000 1.000
D2 0.000 0.000 0.000 1.000
D3 0.000 0.000 0.000 0.000 1.000
D4 0.000 0.000 0.000 0.000 0.000
D5 0.000 0.000 0.000 0.000 0.000
Y0 0.000 0.000 0.000 0.000 0.000
Y1 0.000 0.000 0.000 0.000 0.000
Y2 0.000 0.000 0.000 0.000 0.000
Y3 0.000 0.000 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000 0.000
Y5 0.000 0.000 0.000 0.000 0.000
PSI
D4 D5 Y0 Y1 Y2
________ ________ ________ ________ ________
D4 1.000
D5 0.000 1.000
Y0 0.000 0.000 0.346
Y1 0.000 0.000 0.000 0.324
Y2 0.000 0.000 0.000 0.000 0.484
Y3 0.000 0.000 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000 0.000
Y5 0.000 0.000 0.000 0.000 0.000
PSI
Y3 Y4 Y5
________ ________ ________
Y3 0.584
Y4 0.000 0.985
Y5 0.000 0.000 1.191
Beginning Time: 23:04:54
Ending Time: 23:05:15
Elapsed Time: 00:00:21
MUTHEN & MUTHEN
3463 Stoner Ave.
Los Angeles, CA 90066
Tel: (310) 391-9971
Fax: (310) 391-8971
Web: www.StatModel.com
Support: Support@StatModel.com
Copyright (c) 1998-2022 Muthen & Muthen
Back to examples