Mplus VERSION 6
MUTHEN & MUTHEN
04/25/2010 11:31 PM
INPUT INSTRUCTIONS
title:
web6ex1.inp
montecarlo:
names are y1 y2 y3 y4 x;
nobs=400;
nrep=500;
analysis:
type=random;
model montecarlo:
x@1; [x@0];
eta2 by y3@1 y4*1;
eta2*1;
y3-y4*0.25; !Reliability = 0.80
eta1 on eta2*0.4;
eta1 on x*0.0; !No main effect
eta1*0.5;
eta1 by y1@1 y2*1;
y1-y2*0.25; !Reliability approx 0.80
s | eta1 on x;
s on eta2*0.15; s@0; [s@0]; !This defines s = beta_3 * eta_2
!uncorrelated eta_2 and x
model:
eta2 by y3@1 y4*1;
eta2*1;
y3-y4*0.25; !Reliability = 0.80
eta1 on eta2*0.4;
eta1 on x*0.0; !No main effect
eta1*0.5;
eta1 by y1@1 y2*1;
y1-y2*0.25; !Reliability approx 0.80
s | eta1 on x;
s on eta2*0.15; s@0; [s@0]; !This defines s = beta_3 * eta_2
!uncorrelated eta_2 and x
output:
tech9;
INPUT READING TERMINATED NORMALLY
web6ex1.inp
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 400
Number of replications
Requested 500
Completed 500
Value of seed 0
Number of dependent variables 4
Number of independent variables 1
Number of continuous latent variables 3
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4
Observed independent variables
X
Continuous latent variables
ETA2 ETA1 S
Estimator MLR
Information matrix OBSERVED
Maximum number of iterations 100
Convergence criterion 0.100D-05
Maximum number of EM iterations 500
Convergence criteria for the EM algorithm
Loglikelihood change 0.100D-02
Relative loglikelihood change 0.100D-05
Derivative 0.100D-03
Minimum variance 0.100D-03
Maximum number of steepest descent iterations 20
Optimization algorithm EMA
SAMPLE STATISTICS FOR THE FIRST REPLICATION
ESTIMATED SAMPLE STATISTICS
Means
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
1 -0.022 -0.037 -0.045 -0.007 0.032
Covariances
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
Y1 0.918
Y2 0.714 0.993
Y3 0.390 0.511 1.282
Y4 0.350 0.411 0.955 1.174
X -0.107 -0.127 -0.049 -0.029 0.957
Correlations
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
Y1 1.000
Y2 0.748 1.000
Y3 0.359 0.453 1.000
Y4 0.337 0.381 0.779 1.000
X -0.114 -0.130 -0.044 -0.028 1.000
TESTS OF MODEL FIT
Number of Free Parameters 15
Loglikelihood
H0 Value
Mean -1921.331
Std Dev 27.689
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.994 -1985.743 -1982.798
0.980 0.984 -1978.195 -1977.453
0.950 0.962 -1966.876 -1963.161
0.900 0.910 -1956.817 -1956.343
0.800 0.802 -1944.634 -1944.895
0.700 0.678 -1935.851 -1937.943
0.500 0.476 -1921.331 -1923.418
0.300 0.292 -1906.811 -1907.663
0.200 0.192 -1898.028 -1899.023
0.100 0.112 -1885.845 -1884.244
0.050 0.050 -1875.785 -1875.865
0.020 0.024 -1864.466 -1858.350
0.010 0.016 -1856.918 -1853.754
Information Criteria
Akaike (AIC)
Mean 3872.662
Std Dev 55.378
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.984 3743.837 3735.603
0.980 0.976 3758.933 3746.388
0.950 0.950 3781.571 3781.198
0.900 0.888 3801.690 3796.894
0.800 0.808 3826.056 3826.896
0.700 0.708 3843.622 3844.320
0.500 0.524 3872.662 3876.068
0.300 0.322 3901.702 3905.642
0.200 0.198 3919.267 3919.109
0.100 0.090 3943.633 3940.873
0.050 0.038 3963.752 3956.203
0.020 0.016 3986.390 3978.127
0.010 0.006 4001.486 3993.902
Bayesian (BIC)
Mean 3932.534
Std Dev 55.378
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.984 3803.709 3795.475
0.980 0.976 3818.805 3806.260
0.950 0.950 3841.443 3841.070
0.900 0.888 3861.562 3856.766
0.800 0.808 3885.928 3886.768
0.700 0.708 3903.494 3904.192
0.500 0.524 3932.534 3935.940
0.300 0.322 3961.574 3965.513
0.200 0.198 3979.139 3978.981
0.100 0.090 4003.505 4000.745
0.050 0.038 4023.624 4016.075
0.020 0.016 4046.262 4037.999
0.010 0.006 4061.358 4053.774
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 3884.938
Std Dev 55.378
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.984 3756.113 3747.879
0.980 0.976 3771.209 3758.664
0.950 0.950 3793.847 3793.474
0.900 0.888 3813.966 3809.170
0.800 0.808 3838.332 3839.172
0.700 0.708 3855.898 3856.596
0.500 0.524 3884.938 3888.344
0.300 0.322 3913.978 3917.917
0.200 0.198 3931.543 3931.385
0.100 0.090 3955.909 3953.149
0.050 0.038 3976.028 3968.479
0.020 0.016 3998.666 3990.403
0.010 0.006 4013.762 4006.178
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
ETA2 BY
Y3 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y4 1.000 1.0054 0.0769 0.0784 0.0059 0.962 1.000
ETA1 BY
Y1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 1.000 1.0041 0.0907 0.0919 0.0082 0.952 1.000
ETA1 ON
ETA2 0.400 0.4020 0.0506 0.0491 0.0026 0.930 1.000
S ON
ETA2 0.150 0.1469 0.0437 0.0443 0.0019 0.942 0.912
ETA1 ON
X 0.000 0.0006 0.0401 0.0413 0.0016 0.950 0.050
Intercepts
Y1 0.000 0.0019 0.0480 0.0477 0.0023 0.948 0.052
Y2 0.000 0.0023 0.0457 0.0476 0.0021 0.958 0.042
Y3 0.000 0.0011 0.0564 0.0557 0.0032 0.948 0.052
Y4 0.000 0.0019 0.0556 0.0558 0.0031 0.948 0.052
S 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Variances
ETA2 1.000 0.9942 0.1109 0.1108 0.0123 0.956 1.000
Residual Variances
Y1 0.250 0.2475 0.0579 0.0585 0.0034 0.958 0.976
Y2 0.250 0.2459 0.0591 0.0584 0.0035 0.958 0.958
Y3 0.250 0.2485 0.0722 0.0718 0.0052 0.956 0.894
Y4 0.250 0.2464 0.0730 0.0718 0.0053 0.958 0.902
ETA1 0.500 0.4948 0.0626 0.0649 0.0039 0.938 1.000
S 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.931E-02
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION
NU
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
1 1 2 3 4 0
LAMBDA
ETA2 ETA1 S X
________ ________ ________ ________
Y1 0 0 0 0
Y2 0 5 0 0
Y3 0 0 0 0
Y4 6 0 0 0
X 0 0 0 0
THETA
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
Y1 7
Y2 0 8
Y3 0 0 9
Y4 0 0 0 10
X 0 0 0 0 0
ALPHA
ETA2 ETA1 S X
________ ________ ________ ________
1 0 0 0 0
BETA
ETA2 ETA1 S X
________ ________ ________ ________
ETA2 0 0 0 0
ETA1 11 0 0 12
S 13 0 0 0
X 0 0 0 0
PSI
ETA2 ETA1 S X
________ ________ ________ ________
ETA2 14
ETA1 0 15
S 0 0 0
X 0 0 0 0
STARTING VALUES
NU
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
1 0.000 0.000 0.000 0.000 0.000
LAMBDA
ETA2 ETA1 S X
________ ________ ________ ________
Y1 0.000 1.000 0.000 0.000
Y2 0.000 1.000 0.000 0.000
Y3 1.000 0.000 0.000 0.000
Y4 1.000 0.000 0.000 0.000
X 0.000 0.000 0.000 1.000
THETA
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
Y1 0.250
Y2 0.000 0.250
Y3 0.000 0.000 0.250
Y4 0.000 0.000 0.000 0.250
X 0.000 0.000 0.000 0.000 0.000
ALPHA
ETA2 ETA1 S X
________ ________ ________ ________
1 0.000 0.000 0.000 0.000
BETA
ETA2 ETA1 S X
________ ________ ________ ________
ETA2 0.000 0.000 0.000 0.000
ETA1 0.400 0.000 0.000 0.000
S 0.150 0.000 0.000 0.000
X 0.000 0.000 0.000 0.000
PSI
ETA2 ETA1 S X
________ ________ ________ ________
ETA2 1.000
ETA1 0.000 0.500
S 0.000 0.000 0.000
X 0.000 0.000 0.000 0.500
POPULATION VALUES
NU
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
1 0.000 0.000 0.000 0.000 0.000
LAMBDA
ETA2 ETA1 S X
________ ________ ________ ________
Y1 0.000 1.000 0.000 0.000
Y2 0.000 1.000 0.000 0.000
Y3 1.000 0.000 0.000 0.000
Y4 1.000 0.000 0.000 0.000
X 0.000 0.000 0.000 1.000
THETA
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
Y1 0.250
Y2 0.000 0.250
Y3 0.000 0.000 0.250
Y4 0.000 0.000 0.000 0.250
X 0.000 0.000 0.000 0.000 0.000
ALPHA
ETA2 ETA1 S X
________ ________ ________ ________
1 0.000 0.000 0.000 0.000
BETA
ETA2 ETA1 S X
________ ________ ________ ________
ETA2 0.000 0.000 0.000 0.000
ETA1 0.400 0.000 0.000 0.000
S 0.150 0.000 0.000 0.000
X 0.000 0.000 0.000 0.000
PSI
ETA2 ETA1 S X
________ ________ ________ ________
ETA2 1.000
ETA1 0.000 0.500
S 0.000 0.000 0.000
X 0.000 0.000 0.000 1.000
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
Beginning Time: 23:31:31
Ending Time: 23:34:29
Elapsed Time: 00:02:58
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