Mplus VERSION 7.4
MUTHEN & MUTHEN
06/03/2016 3:37 PM
INPUT INSTRUCTIONS
title:
Measurement error in M
with reliability 0.7
montecarlo:
names = y m x;
nobs = 400;
nreps = 500;
cutpoints = x(0);
model population:
x@1; ! V(dich'd x) = 0.5*0.5 = 0.25
eta by m@1;
eta on x*.5;
eta*.1458; ! V(eta) = 0.0625+0.1458=0.2083, R2(eta) = 0.3
m*.0893; ! Reliability of m = 0.7
y on eta*.5 x*.3;
y*.8879; ! V(y) = 0.112075+0.8879 = 1, R2(y) = 0.11
analysis:
model:
m on x*.5 (b);
y on m*.5 (a)
x*.3;
m*.0893;
y*.8879;
[y*0];
[m*0];
model constraint:
new(ind*.25);
ind = a*b;
output:
INPUT READING TERMINATED NORMALLY
Measurement error in M
with reliability 0.7
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 2
Number of independent variables 1
Number of continuous latent variables 0
Observed dependent variables
Continuous
Y M
Observed independent variables
X
Estimator ML
Information matrix OBSERVED
Maximum number of iterations 1000
Convergence criterion 0.500D-04
Maximum number of steepest descent iterations 20
SAMPLE STATISTICS FOR THE FIRST REPLICATION
SAMPLE STATISTICS
Means
Y M X
________ ________ ________
1 0.305 0.254 0.487
Covariances
Y M X
________ ________ ________
Y 0.992
M 0.172 0.298
X 0.156 0.117 0.250
Correlations
Y M X
________ ________ ________
Y 1.000
M 0.317 1.000
X 0.312 0.428 1.000
MODEL FIT INFORMATION
Number of Free Parameters 7
Loglikelihood
H0 Value
Mean -822.412
Std Dev 18.926
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.992 -866.440 -866.138
0.980 0.982 -861.281 -860.486
0.950 0.958 -853.544 -852.108
0.900 0.904 -846.668 -846.588
0.800 0.796 -838.340 -838.885
0.700 0.706 -832.337 -832.090
0.500 0.496 -822.412 -822.796
0.300 0.290 -812.487 -813.288
0.200 0.202 -806.484 -806.423
0.100 0.096 -798.156 -798.303
0.050 0.060 -791.280 -790.008
0.020 0.024 -783.543 -781.651
0.010 0.010 -778.384 -778.525
H1 Value
Mean -822.412
Std Dev 18.926
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.992 -866.440 -866.138
0.980 0.982 -861.281 -860.486
0.950 0.958 -853.544 -852.108
0.900 0.904 -846.668 -846.588
0.800 0.796 -838.340 -838.885
0.700 0.706 -832.337 -832.090
0.500 0.496 -822.412 -822.796
0.300 0.290 -812.487 -813.288
0.200 0.202 -806.484 -806.423
0.100 0.096 -798.156 -798.303
0.050 0.060 -791.280 -790.008
0.020 0.024 -783.543 -781.651
0.010 0.010 -778.384 -778.525
Information Criteria
Akaike (AIC)
Mean 1658.824
Std Dev 37.852
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.990 1570.768 1568.611
0.980 0.976 1581.086 1577.254
0.950 0.940 1596.560 1591.683
0.900 0.904 1610.312 1610.328
0.800 0.798 1626.967 1625.885
0.700 0.710 1638.974 1640.360
0.500 0.504 1658.824 1659.490
0.300 0.294 1678.674 1677.868
0.200 0.204 1690.680 1691.665
0.100 0.096 1707.335 1706.751
0.050 0.042 1721.087 1717.737
0.020 0.018 1736.561 1734.639
0.010 0.008 1746.880 1740.174
Bayesian (BIC)
Mean 1686.764
Std Dev 37.852
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.990 1598.708 1596.552
0.980 0.976 1609.027 1605.194
0.950 0.940 1624.501 1619.624
0.900 0.904 1638.252 1638.269
0.800 0.798 1654.907 1653.825
0.700 0.710 1666.914 1668.300
0.500 0.504 1686.764 1687.430
0.300 0.294 1706.614 1705.808
0.200 0.204 1718.621 1719.605
0.100 0.096 1735.276 1734.691
0.050 0.042 1749.027 1745.678
0.020 0.018 1764.501 1762.579
0.010 0.008 1774.820 1768.114
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 1664.553
Std Dev 37.852
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.990 1576.497 1574.340
0.980 0.976 1586.815 1582.983
0.950 0.940 1602.289 1597.412
0.900 0.904 1616.041 1616.057
0.800 0.798 1632.696 1631.613
0.700 0.710 1644.703 1646.089
0.500 0.504 1664.553 1665.219
0.300 0.294 1684.402 1683.596
0.200 0.204 1696.409 1697.393
0.100 0.096 1713.064 1712.480
0.050 0.042 1726.816 1723.466
0.020 0.018 1742.290 1740.367
0.010 0.008 1752.608 1745.903
Chi-Square Test of Model Fit
Degrees of freedom 0
Mean 0.000
Std Dev 0.000
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 0.000 0.000
0.980 1.000 0.000 0.000
0.950 1.000 0.000 0.000
0.900 1.000 0.000 0.000
0.800 1.000 0.000 0.000
0.700 1.000 0.000 0.000
0.500 1.000 0.000 0.000
0.300 1.000 0.000 0.000
0.200 1.000 0.000 0.000
0.100 1.000 0.000 0.000
0.050 1.000 0.000 0.000
0.020 1.000 0.000 0.000
0.010 1.000 0.000 0.000
RMSEA (Root Mean Square Error Of Approximation)
Mean 0.000
Std Dev 0.000
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 0.000 0.000
0.980 0.000 0.000 0.000
0.950 0.000 0.000 0.000
0.900 0.000 0.000 0.000
0.800 0.000 0.000 0.000
0.700 0.000 0.000 0.000
0.500 0.000 0.000 0.000
0.300 0.000 0.000 0.000
0.200 0.000 0.000 0.000
0.100 0.000 0.000 0.000
0.050 0.000 0.000 0.000
0.020 0.000 0.000 0.000
0.010 0.000 0.000 0.000
SRMR (Standardized Root Mean Square Residual)
Mean 0.000
Std Dev 0.000
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.954 0.000 0.000
0.980 0.954 0.000 0.000
0.950 0.954 0.000 0.000
0.900 0.952 0.000 0.000
0.800 0.942 0.000 0.000
0.700 0.880 0.000 0.000
0.500 0.620 0.000 0.000
0.300 0.270 0.000 0.000
0.200 0.068 0.000 0.000
0.100 0.002 0.000 0.000
0.050 0.000 0.000 0.000
0.020 0.000 0.000 0.000
0.010 0.000 0.000 0.000
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
M ON
X 0.500 0.4983 0.0496 0.0484 0.0025 0.942 1.000
Y ON
M 0.500 0.3071 0.1024 0.0980 0.0477 0.488 0.876
X 0.300 0.4020 0.1068 0.1068 0.0218 0.832 0.962
Intercepts
Y 0.000 0.0016 0.0694 0.0670 0.0048 0.944 0.056
M 0.000 -0.0004 0.0359 0.0342 0.0013 0.940 0.060
Residual Variances
Y 0.888 0.8981 0.0608 0.0635 0.0038 0.958 1.000
M 0.089 0.2342 0.0167 0.0166 0.0213 0.000 1.000
New/Additional Parameters
IND 0.250 0.1526 0.0524 0.0513 0.0122 0.502 0.868
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.268E-03
(ratio of smallest to largest eigenvalue)
TECHNICAL OUTPUT
PARAMETER SPECIFICATION
NU
Y M X
________ ________ ________
1 0 0 0
LAMBDA
Y M X
________ ________ ________
Y 0 0 0
M 0 0 0
X 0 0 0
THETA
Y M X
________ ________ ________
Y 0
M 0 0
X 0 0 0
ALPHA
Y M X
________ ________ ________
1 1 2 0
BETA
Y M X
________ ________ ________
Y 0 3 4
M 0 0 5
X 0 0 0
PSI
Y M X
________ ________ ________
Y 6
M 0 7
X 0 0 0
PARAMETER SPECIFICATION FOR THE ADDITIONAL PARAMETERS
New/Additional Parameters
IND
________
1 8
STARTING VALUES
NU
Y M X
________ ________ ________
1 0.000 0.000 0.000
LAMBDA
Y M X
________ ________ ________
Y 1.000 0.000 0.000
M 0.000 1.000 0.000
X 0.000 0.000 1.000
THETA
Y M X
________ ________ ________
Y 0.000
M 0.000 0.000
X 0.000 0.000 0.000
ALPHA
Y M X
________ ________ ________
1 0.000 0.000 0.487
BETA
Y M X
________ ________ ________
Y 0.000 0.500 0.300
M 0.000 0.000 0.500
X 0.000 0.000 0.000
PSI
Y M X
________ ________ ________
Y 0.888
M 0.000 0.089
X 0.000 0.000 0.250
STARTING VALUES FOR THE ADDITIONAL PARAMETERS
New/Additional Parameters
IND
________
1 0.250
POPULATION VALUES
NU
Y M X
________ ________ ________
1 0.000 0.000 0.000
LAMBDA
ETA Y X
________ ________ ________
Y 0.000 1.000 0.000
M 1.000 0.000 0.000
X 0.000 0.000 1.000
THETA
Y M X
________ ________ ________
Y 0.000
M 0.000 0.089
X 0.000 0.000 0.000
ALPHA
ETA Y X
________ ________ ________
1 0.000 0.000 0.000
BETA
ETA Y X
________ ________ ________
ETA 0.000 0.000 0.500
Y 0.500 0.000 0.300
X 0.000 0.000 0.000
PSI
ETA Y X
________ ________ ________
ETA 0.146
Y 0.000 0.888
X 0.000 0.000 1.000
DIAGRAM INFORMATION
Mplus diagrams are currently not available for Monte Carlo analysis.
No diagram output was produced.
Beginning Time: 15:37:05
Ending Time: 15:37:06
Elapsed Time: 00:00:01
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