Mplus VERSION 7.4
MUTHEN & MUTHEN
06/03/2016 3:05 PM
INPUT INSTRUCTIONS
title:
Generate as M on X, Y on M and X
adding a residual correlation of rho=0.30
Analyze as M on X, Y on X
Using Imai formulas for sensitivity analysis
montecarlo:
names = y m x;
nobs = 400;
nreps = 500;
cutpoints = x(0);
model population:
x@1;
[y*1]; ! beta0
y on m*.5 ! beta1
x*.4; ! beta2
[m*2]; ! gamma0
m on x*.5; ! gamma1
y*.5; ! sig1-squared
m*1; ! sig2-squared
y with m*.2121; ! gives res corr 0.30
analysis:
model:
[y] (kappa0);
y on x (kappa1);
[m*2] (gamma0);
m on x*.5 (gamma1);
y (sig); ! sig-squared
m*1 (sig2); ! sig2-squared
y with m (cov);
model constraint:
new(rho*.30 rhocurl
beta1*.5 beta2*.4 beta0*1 sig1*.7071 ind*.25 de*.4);
rhocurl=cov/(sqrt(sig)*sqrt(sig2));
rho=.30;
beta1=(sqrt(sig)/sqrt(sig2))*
(rhocurl-rho*sqrt((1-rhocurl*rhocurl)/(1-rho*rho)));
beta2=kappa1-beta1*gamma1;
beta0=kappa0-beta1*gamma0;
sig1=(rhocurl*sqrt(sig)-beta1*sqrt(sig2))/rho;
ind=beta1*gamma1;
de=beta2;
INPUT READING TERMINATED NORMALLY
Generate as M on X, Y on M and X
adding a residual correlation of rho=0.30
Analyze as M on X, Y on X
Using Imai formulas for sensitivity analysis
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 2.354 2.281 0.487
Covariances
Y M X
________ ________ ________
Y 1.062
M 0.822 1.117
X 0.181 0.125 0.250
Correlations
Y M X
________ ________ ________
Y 1.000
M 0.755 1.000
X 0.351 0.237 1.000
MODEL FIT INFORMATION
Number of Free Parameters 7
Loglikelihood
H0 Value
Mean -975.160
Std Dev 18.926
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.992 -1019.188 -1018.886
0.980 0.982 -1014.029 -1013.234
0.950 0.958 -1006.291 -1004.856
0.900 0.904 -999.416 -999.336
0.800 0.796 -991.088 -991.633
0.700 0.706 -985.085 -984.837
0.500 0.496 -975.160 -975.544
0.300 0.290 -965.235 -966.036
0.200 0.202 -959.232 -959.171
0.100 0.096 -950.904 -951.051
0.050 0.060 -944.028 -942.756
0.020 0.024 -936.291 -934.399
0.010 0.010 -931.132 -931.273
H1 Value
Mean -975.160
Std Dev 18.926
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.992 -1019.188 -1018.886
0.980 0.982 -1014.028 -1013.234
0.950 0.958 -1006.291 -1004.856
0.900 0.904 -999.416 -999.336
0.800 0.796 -991.088 -991.633
0.700 0.706 -985.085 -984.837
0.500 0.496 -975.160 -975.544
0.300 0.290 -965.235 -966.036
0.200 0.202 -959.232 -959.171
0.100 0.096 -950.904 -951.051
0.050 0.060 -944.028 -942.756
0.020 0.024 -936.291 -934.399
0.010 0.010 -931.132 -931.273
Information Criteria
Akaike (AIC)
Mean 1964.320
Std Dev 37.852
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.990 1876.264 1874.107
0.980 0.976 1886.582 1882.750
0.950 0.940 1902.056 1897.179
0.900 0.904 1915.808 1915.824
0.800 0.798 1932.463 1931.380
0.700 0.710 1944.470 1945.856
0.500 0.504 1964.320 1964.986
0.300 0.294 1984.169 1983.363
0.200 0.204 1996.176 1997.160
0.100 0.096 2012.831 2012.247
0.050 0.042 2026.583 2023.233
0.020 0.018 2042.057 2040.135
0.010 0.008 2052.376 2045.670
Bayesian (BIC)
Mean 1992.260
Std Dev 37.852
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.990 1904.204 1902.047
0.980 0.976 1914.523 1910.690
0.950 0.940 1929.997 1925.120
0.900 0.904 1943.748 1943.764
0.800 0.798 1960.403 1959.321
0.700 0.710 1972.410 1973.796
0.500 0.504 1992.260 1992.926
0.300 0.294 2012.110 2011.304
0.200 0.204 2024.116 2025.101
0.100 0.096 2040.771 2040.187
0.050 0.042 2054.523 2051.174
0.020 0.018 2069.997 2068.075
0.010 0.008 2080.316 2073.610
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 1970.048
Std Dev 37.852
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.990 1881.992 1879.836
0.980 0.976 1892.311 1888.479
0.950 0.940 1907.785 1902.908
0.900 0.904 1921.537 1921.553
0.800 0.798 1938.192 1937.109
0.700 0.710 1950.199 1951.584
0.500 0.504 1970.048 1970.714
0.300 0.294 1989.898 1989.092
0.200 0.204 2001.905 2002.889
0.100 0.096 2018.560 2017.976
0.050 0.042 2032.312 2028.962
0.020 0.018 2047.786 2045.863
0.010 0.008 2058.104 2051.399
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 1.000 0.000 0.000
0.980 1.000 0.000 0.000
0.950 0.900 0.000 0.000
0.900 0.762 0.000 0.000
0.800 0.712 0.000 0.000
0.700 0.698 0.000 0.000
0.500 0.688 0.000 0.000
0.300 0.480 0.000 0.000
0.200 0.118 0.000 0.000
0.100 0.018 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
Y ON
X 0.000 0.6551 0.0994 0.0981 0.4390 0.000 1.000
M ON
X 0.500 0.5008 0.1033 0.0998 0.0107 0.952 1.000
Y WITH
M 0.000 0.7095 0.0614 0.0604 0.5072 0.000 1.000
Intercepts
Y 0.000 2.0016 0.0721 0.0692 4.0117 0.000 1.000
M 2.000 2.0004 0.0752 0.0705 0.0056 0.940 1.000
Residual Variances
Y 0.500 0.9603 0.0661 0.0679 0.2162 0.000 1.000
M 1.000 0.9957 0.0713 0.0704 0.0051 0.958 1.000
New/Additional Parameters
RHO 0.300 0.3000 0.0000 0.0000 0.0000 0.000 1.000
RHOCURL 0.500 0.7251 0.0245 0.0237 0.0513 0.000 1.000
BETA1 0.500 0.5001 0.0366 0.0354 0.0013 0.928 1.000
BETA2 0.400 0.4048 0.0732 0.0729 0.0054 0.938 1.000
BETA0 1.000 1.0012 0.0892 0.0867 0.0079 0.944 1.000
SIG1 0.707 0.7055 0.0242 0.0249 0.0006 0.948 1.000
IND 0.250 0.2502 0.0544 0.0532 0.0030 0.952 1.000
DE 0.400 0.4048 0.0732 0.0729 0.0054 0.938 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.242E-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 0 3
M 0 0 4
X 0 0 0
PSI
Y M X
________ ________ ________
Y 5
M 6 7
X 0 0 0
PARAMETER SPECIFICATION FOR THE ADDITIONAL PARAMETERS
New/Additional Parameters
RHO RHOCURL BETA1 BETA2 BETA0
________ ________ ________ ________ ________
1 8 9 10 11 12
New/Additional Parameters
SIG1 IND DE
________ ________ ________
1 13 14 15
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 2.000 0.487
BETA
Y M X
________ ________ ________
Y 0.000 0.000 0.000
M 0.000 0.000 0.500
X 0.000 0.000 0.000
PSI
Y M X
________ ________ ________
Y 0.500
M 0.000 1.000
X 0.000 0.000 0.250
STARTING VALUES FOR THE ADDITIONAL PARAMETERS
New/Additional Parameters
RHO RHOCURL BETA1 BETA2 BETA0
________ ________ ________ ________ ________
1 0.300 0.500 0.500 0.400 1.000
New/Additional Parameters
SIG1 IND DE
________ ________ ________
1 0.707 0.250 0.400
POPULATION 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 1.000 2.000 0.000
BETA
Y M X
________ ________ ________
Y 0.000 0.500 0.400
M 0.000 0.000 0.500
X 0.000 0.000 0.000
PSI
Y M X
________ ________ ________
Y 0.500
M 0.212 1.000
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: 15:05:04
Ending Time: 15:05:10
Elapsed Time: 00:00:06
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