Mplus VERSION 7.4
MUTHEN & MUTHEN
06/02/2016 6:18 AM
INPUT INSTRUCTIONS
title:
Selection modeling
Muthen-Joreskog (1983), p. 146
with data generated similar to Model 1, p. 158
y missing if u=0
montecarlo:
names = y u x;
nobs = 4000;
nreps = 500;
categorical = u; ! u = 1 if y observed
generate = u(1 p);
missing = y;
model population:
x@1;
y on x*1;
[y*0];
y*1;
f by y*-1 u@1; ! gives residual corr = -0.5
f@1;
u on x*-1;
analysis:
estimator = mlr;
link = probit;
processors = 8;
mconvergence = 0.00001;
integration = 30;
model:
y on x*1;
[y*0];
y*1 (v);
f by y*-1 (lam)
u@1; ! gives -0.5 res. correlation
f@1;
u on x*-1 (slope);
[u$1] (thresh);
model missing:
! binary y = 1 denotes missing on continuous y
! logit regression for y with [y] denoting intercept
[y@15]; ! probability one of missing on y if u = 0
y on u@-30; ! probability zero of missing on y if u=1
model constraint:
new (rescorr*-.5 probint*0 probslop*-0.707107);
rescorr = lam/(sqrt(lam*lam+v)*sqrt(1+1));
probint = -thresh/sqrt(1+1);
probslop = slope/sqrt(1+1);
output:
tech9;
INPUT READING TERMINATED NORMALLY
Selection modeling
Muthen-Joreskog (1983), p. 146
with data generated similar to Model 1, p. 158
y missing if u=0
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 4000
Number of replications
Requested 500
Completed 499
Value of seed 0
Number of dependent variables 2
Number of independent variables 1
Number of continuous latent variables 1
Observed dependent variables
Continuous
Y
Binary and ordered categorical (ordinal)
U
Observed independent variables
X
Continuous latent variables
F
Estimator MLR
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-04
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 10
Minimum value for logit thresholds -10
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 STANDARD
Number of integration points 30
Dimensions of numerical integration 1
Adaptive quadrature ON
Link PROBIT
Cholesky ON
SUMMARY OF DATA FOR THE FIRST REPLICATION
Number of missing data patterns 2
Number of y missing data patterns 2
Number of u missing data patterns 1
SUMMARY OF MISSING DATA PATTERNS FOR THE FIRST REPLICATION
MISSING DATA PATTERNS FOR Y (x = not missing)
1 2
Y x
X x x
MISSING DATA PATTERN FREQUENCIES FOR Y
Pattern Frequency Pattern Frequency
1 1916 2 2084
COVARIANCE COVERAGE OF DATA FOR THE FIRST REPLICATION
Minimum covariance coverage value 0.100
PROPORTION OF DATA PRESENT FOR Y
Covariance Coverage
Y X
________ ________
Y 0.479
X 0.479 1.000
SAMPLE STATISTICS FOR THE FIRST REPLICATION
ESTIMATED SAMPLE STATISTICS
Means
Y X
________ ________
1 -0.618 0.023
Covariances
Y X
________ ________
Y 2.313
X 0.735 1.041
Correlations
Y X
________ ________
Y 1.000
X 0.474 1.000
MAXIMUM LOG-LIKELIHOOD VALUE FOR THE UNRESTRICTED (H1) MODEL IS -9035.653
MODEL FIT INFORMATION
Number of Free Parameters 6
Loglikelihood
H0 Value
Mean -5678.191
Std Dev 65.682
Number of successful computations 499
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.986 -5830.988 -5879.058
0.980 0.978 -5813.083 -5819.083
0.950 0.950 -5786.232 -5787.180
0.900 0.908 -5762.370 -5761.261
0.800 0.796 -5733.469 -5735.578
0.700 0.703 -5712.635 -5712.537
0.500 0.509 -5678.191 -5677.147
0.300 0.303 -5643.748 -5643.563
0.200 0.188 -5622.913 -5626.643
0.100 0.092 -5594.013 -5598.251
0.050 0.048 -5570.151 -5571.426
0.020 0.016 -5543.300 -5549.972
0.010 0.010 -5525.395 -5529.955
Information Criteria
Akaike (AIC)
Mean 11368.383
Std Dev 131.364
Number of successful computations 499
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.990 11062.791 11057.027
0.980 0.984 11098.600 11103.231
0.950 0.952 11152.302 11141.701
0.900 0.908 11200.027 11205.712
0.800 0.812 11257.827 11261.583
0.700 0.697 11299.496 11295.978
0.500 0.491 11368.383 11365.334
0.300 0.297 11437.270 11434.447
0.200 0.204 11478.939 11480.230
0.100 0.092 11536.739 11531.103
0.050 0.050 11584.464 11583.108
0.020 0.022 11638.165 11642.066
0.010 0.014 11673.975 11743.840
Bayesian (BIC)
Mean 11406.147
Std Dev 131.364
Number of successful computations 499
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.990 11100.555 11094.792
0.980 0.984 11136.365 11140.995
0.950 0.952 11190.066 11179.465
0.900 0.908 11237.791 11243.476
0.800 0.812 11295.591 11299.347
0.700 0.697 11337.260 11333.742
0.500 0.491 11406.147 11403.098
0.300 0.297 11475.034 11472.211
0.200 0.204 11516.703 11517.994
0.100 0.092 11574.503 11568.868
0.050 0.050 11622.228 11620.872
0.020 0.022 11675.930 11679.830
0.010 0.014 11711.739 11781.605
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 11387.082
Std Dev 131.364
Number of successful computations 499
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.990 11081.490 11075.726
0.980 0.984 11117.299 11121.930
0.950 0.952 11171.001 11160.400
0.900 0.908 11218.726 11224.411
0.800 0.812 11276.526 11280.282
0.700 0.697 11318.194 11314.677
0.500 0.491 11387.082 11384.033
0.300 0.297 11455.969 11453.146
0.200 0.204 11497.638 11498.929
0.100 0.092 11555.438 11549.802
0.050 0.050 11603.163 11601.807
0.020 0.022 11656.864 11660.765
0.010 0.014 11692.674 11762.539
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
F BY
Y -1.000 -0.9723 0.3049 0.2869 0.0935 0.908 0.858
U 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y ON
X 1.000 0.9917 0.0894 0.0863 0.0081 0.924 0.992
U ON
X -1.000 -1.0004 0.0355 0.0356 0.0013 0.942 1.000
Intercepts
Y 0.000 -0.0150 0.1818 0.1724 0.0332 0.914 0.086
Thresholds
U$1 0.000 0.0000 0.0296 0.0303 0.0009 0.952 0.048
Variances
F 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Residual Variances
Y 1.000 0.9738 0.3612 0.3670 0.1309 0.886 0.691
New/Additional Parameters
RESCORR -0.500 -0.4809 0.1406 0.1277 0.0201 0.906 0.874
PROBINT 0.000 0.0000 0.0210 0.0215 0.0004 0.952 0.048
PROBSLOP -0.707 -0.7074 0.0251 0.0251 0.0006 0.942 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.257E-03
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION
TAU
U$1
________
1 6
NU
U Y X
________ ________ ________
1 0 0 0
LAMBDA
F U Y X
________ ________ ________ ________
U 0 0 0 0
Y 0 0 0 0
X 0 0 0 0
THETA
U Y X
________ ________ ________
U 0
Y 0 0
X 0 0 0
ALPHA
F U Y X
________ ________ ________ ________
1 0 0 1 0
BETA
F U Y X
________ ________ ________ ________
F 0 0 0 0
U 0 0 0 2
Y 3 0 0 4
X 0 0 0 0
PSI
F U Y X
________ ________ ________ ________
F 0
U 0 0
Y 0 0 5
X 0 0 0 0
PARAMETER SPECIFICATION FOR THE ADDITIONAL PARAMETERS
NEW/ADDITIONAL PARAMETERS
RESCORR PROBINT PROBSLOP
________ ________ ________
1 7 8 9
STARTING VALUES
TAU
U$1
________
1 0.000
NU
U Y X
________ ________ ________
1 0.000 0.000 0.000
LAMBDA
F U Y X
________ ________ ________ ________
U 0.000 1.000 0.000 0.000
Y 0.000 0.000 1.000 0.000
X 0.000 0.000 0.000 1.000
THETA
U Y X
________ ________ ________
U 0.000
Y 0.000 0.000
X 0.000 0.000 0.000
ALPHA
F U Y X
________ ________ ________ ________
1 0.000 0.000 0.000 0.000
BETA
F U Y X
________ ________ ________ ________
F 0.000 0.000 0.000 0.000
U 1.000 0.000 0.000 -1.000
Y -1.000 0.000 0.000 1.000
X 0.000 0.000 0.000 0.000
PSI
F U Y X
________ ________ ________ ________
F 1.000
U 0.000 1.000
Y 0.000 0.000 1.000
X 0.000 0.000 0.000 0.500
STARTING VALUES FOR THE ADDITIONAL PARAMETERS
NEW/ADDITIONAL PARAMETERS
RESCORR PROBINT PROBSLOP
________ ________ ________
1 -0.500 0.000 -0.707
POPULATION VALUES
TAU
U$1
________
1 0.000
NU
U Y X
________ ________ ________
1 0.000 0.000 0.000
LAMBDA
F U Y X
________ ________ ________ ________
U 0.000 1.000 0.000 0.000
Y 0.000 0.000 1.000 0.000
X 0.000 0.000 0.000 1.000
THETA
U Y X
________ ________ ________
U 0.000
Y 0.000 0.000
X 0.000 0.000 0.000
ALPHA
F U Y X
________ ________ ________ ________
1 0.000 0.000 0.000 0.000
BETA
F U Y X
________ ________ ________ ________
F 0.000 0.000 0.000 0.000
U 1.000 0.000 0.000 -1.000
Y -1.000 0.000 0.000 1.000
X 0.000 0.000 0.000 0.000
PSI
F U Y X
________ ________ ________ ________
F 1.000
U 0.000 0.000
Y 0.000 0.000 1.000
X 0.000 0.000 0.000 1.000
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
REPLICATION 334:
THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO A NON-ZERO
DERIVATIVE OF THE OBSERVED-DATA LOGLIKELIHOOD.
THE MCONVERGENCE CRITERION OF THE EM ALGORITHM IS NOT FULFILLED.
CHECK YOUR STARTING VALUES OR INCREASE THE NUMBER OF MITERATIONS.
ESTIMATES CANNOT BE TRUSTED. THE LOGLIKELIHOOD DERIVATIVE
FOR THE FOLLOWING PARAMETER IS -0.24252797D-03:
Parameter 5, Y (equality/label)
DIAGRAM INFORMATION
Mplus diagrams are currently not available for Monte Carlo analysis.
No diagram output was produced.
Beginning Time: 06:18:12
Ending Time: 06:29:12
Elapsed Time: 00:11:00
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) 1998-2015 Muthen & Muthen
Back to examples