```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;

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

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

RHO           RHOCURL       BETA1         BETA2         BETA0
________      ________      ________      ________      ________
1                  8             9            10            11            12

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

RHO           RHOCURL       BETA1         BETA2         BETA0
________      ________      ________      ________      ________
1              0.300         0.500         0.500         0.400         1.000

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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Los Angeles, CA  90066

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Fax: (310) 391-8971
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