```Mplus VERSION 7.4
MUTHEN & MUTHEN
06/03/2016   3:02 PM

INPUT INSTRUCTIONS

title:
Step 2
Simulating Z moderation of X to M using a random slope,
saving the data for external Monte Carlo analysis
Data:
file xzreplist.dat;
type = montecarlo;

Variable:
names = y m x z;
usevariables = y m x z xz;

Define:
xz = x*z;

Analysis:
estimator = mlr;

model:
y on m*.5 (b)
x*.2 z*.1;
y*.5; [y*0];
m on x*.3 (gamma1);
m on z*.3;
m on xz*.2 (gamma3);
m*.5; [m*0];

model constraint:
new(indavg*.15 indlow*.05 indhigh*.25);
indavg = b*gamma1;
indlow = b*(gamma1-gamma3);
indhigh = b*(gamma1+gamma3);

Step 2
Simulating Z moderation of X to M using a random slope,
saving the data for external Monte Carlo analysis

SUMMARY OF ANALYSIS

Number of groups                                                 1
Average number of observations                                 400

Number of replications
Requested                                                  500
Completed                                                  500

Number of dependent variables                                    2
Number of independent variables                                  3
Number of continuous latent variables                            0

Observed dependent variables

Continuous
Y           M

Observed independent variables
X           Z           XZ

Estimator                                                      MLR
Information matrix                                        OBSERVED
Maximum number of iterations                                  1000
Convergence criterion                                    0.500D-04
Maximum number of steepest descent iterations                   20

Input data file(s)
Multiple data files from
xzreplist.dat

Input data format  FREE

SAMPLE STATISTICS

NOTE:  These are average results over 500 data sets.

SAMPLE STATISTICS

Means
Y             M             X             Z             XZ
________      ________      ________      ________      ________
1              0.197         0.190         0.500         0.002         0.202

Covariances
Y             M             X             Z             XZ
________      ________      ________      ________      ________
Y              0.787
M              0.446         0.737
X              0.148         0.155         0.249
Z              0.368         0.460         0.200         0.999
XZ             0.205         0.273         0.101         0.500         0.460

Correlations
Y             M             X             Z             XZ
________      ________      ________      ________      ________
Y              1.000
M              0.585         1.000
X              0.335         0.362         1.000
Z              0.415         0.536         0.402         1.000
XZ             0.340         0.468         0.297         0.738         1.000

MODEL FIT INFORMATION

Number of Free Parameters                       10

Loglikelihood

H0 Value

Mean                              -852.092
Std Dev                             19.695
Number of successful computations      500

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.994         -897.908       -897.068
0.980       0.982         -892.539       -891.919
0.950       0.956         -884.488       -883.799
0.900       0.914         -877.333       -876.733
0.800       0.788         -868.667       -869.651
0.700       0.694         -862.420       -862.759
0.500       0.484         -852.092       -853.131
0.300       0.294         -841.764       -842.159
0.200       0.194         -835.517       -835.998
0.100       0.110         -826.851       -826.193
0.050       0.056         -819.696       -819.524
0.020       0.016         -811.645       -814.454
0.010       0.008         -806.276       -807.065

H1 Value

Mean                              -851.610
Std Dev                             19.731
Number of successful computations      500

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.994         -897.511       -896.413
0.980       0.982         -892.133       -891.905
0.950       0.958         -884.066       -882.982
0.900       0.908         -876.898       -876.282
0.800       0.786         -868.216       -869.245
0.700       0.700         -861.957       -862.273
0.500       0.484         -851.610       -852.214
0.300       0.296         -841.263       -841.495
0.200       0.196         -835.004       -835.617
0.100       0.106         -826.322       -825.459
0.050       0.050         -819.154       -819.211
0.020       0.018         -811.088       -813.054
0.010       0.006         -805.709       -806.934

Information Criteria

Akaike (AIC)

Mean                              1724.184
Std Dev                             39.389
Number of successful computations      500

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.992         1632.553       1633.887
0.980       0.984         1643.290       1647.598
0.950       0.944         1659.393       1659.016
0.900       0.890         1673.703       1671.094
0.800       0.806         1691.034       1691.907
0.700       0.706         1703.529       1704.232
0.500       0.516         1724.184       1726.100
0.300       0.306         1744.840       1745.511
0.200       0.212         1757.335       1758.910
0.100       0.086         1774.666       1772.917
0.050       0.044         1788.976       1787.428
0.020       0.018         1805.079       1803.239
0.010       0.006         1815.816       1813.616

Bayesian (BIC)

Mean                              1764.099
Std Dev                             39.389
Number of successful computations      500

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.992         1672.467       1673.801
0.980       0.984         1683.205       1687.513
0.950       0.944         1699.307       1698.930
0.900       0.890         1713.617       1711.009
0.800       0.806         1730.949       1731.822
0.700       0.706         1743.443       1744.147
0.500       0.516         1764.099       1766.014
0.300       0.306         1784.755       1785.425
0.200       0.212         1797.249       1798.824
0.100       0.086         1814.581       1812.831
0.050       0.044         1828.891       1827.343
0.020       0.018         1844.993       1843.153
0.010       0.006         1855.731       1853.531

Sample-Size Adjusted BIC (n* = (n + 2) / 24)

Mean                              1732.368
Std Dev                             39.389
Number of successful computations      500

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.992         1640.737       1642.070
0.980       0.984         1651.474       1655.782
0.950       0.944         1667.577       1667.199
0.900       0.890         1681.887       1679.278
0.800       0.806         1699.218       1700.091
0.700       0.706         1711.713       1712.416
0.500       0.516         1732.368       1734.284
0.300       0.306         1753.024       1753.695
0.200       0.212         1765.519       1767.094
0.100       0.086         1782.850       1781.101
0.050       0.044         1797.160       1795.612
0.020       0.018         1813.263       1811.423
0.010       0.006         1824.000       1821.800

Chi-Square Test of Model Fit

Degrees of freedom                       1

Mean                                 0.991
Std Dev                              1.478
Number of successful computations      500

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.988            0.000          0.000
0.980       0.982            0.001          0.001
0.950       0.952            0.004          0.004
0.900       0.904            0.016          0.017
0.800       0.808            0.064          0.070
0.700       0.698            0.148          0.146
0.500       0.510            0.455          0.481
0.300       0.272            1.074          0.981
0.200       0.174            1.642          1.453
0.100       0.094            2.706          2.583
0.050       0.052            3.841          3.852
0.020       0.022            5.412          5.486
0.010       0.016            6.635          8.258

RMSEA (Root Mean Square Error Of Approximation)

Mean                                 0.016
Std Dev                              0.030
Number of successful computations      500

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       1.000           -0.055          0.000
0.980       1.000           -0.047          0.000
0.950       1.000           -0.034          0.000
0.900       1.000           -0.023          0.000
0.800       1.000           -0.010          0.000
0.700       1.000            0.000          0.000
0.500       0.268            0.016          0.000
0.300       0.210            0.032          0.000
0.200       0.172            0.042          0.034
0.100       0.126            0.055          0.063
0.050       0.094            0.066          0.084
0.020       0.064            0.078          0.106
0.010       0.048            0.087          0.135

CFI/TLI

CFI

Mean                                 0.999
Std Dev                              0.004
Number of successful computations      500

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.960            0.990          0.980
0.980       0.952            0.991          0.986
0.950       0.930            0.993          0.991
0.900       0.916            0.994          0.995
0.800       0.888            0.996          0.999
0.700       0.872            0.997          1.000
0.500       0.802            0.999          1.000
0.300       0.000            1.000          1.000
0.200       0.000            1.002          1.000
0.100       0.000            1.003          1.000
0.050       0.000            1.004          1.000
0.020       0.000            1.006          1.000
0.010       0.000            1.007          1.000

TLI

Mean                                 1.000
Std Dev                              0.030
Number of successful computations      500

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.962            0.931          0.863
0.980       0.950            0.939          0.902
0.950       0.930            0.951          0.939
0.900       0.908            0.962          0.964
0.800       0.876            0.975          0.990
0.700       0.838            0.985          1.000
0.500       0.698            1.000          1.011
0.300       0.346            1.016          1.017
0.200       0.008            1.025          1.018
0.100       0.000            1.039          1.021
0.050       0.000            1.049          1.022
0.020       0.000            1.062          1.024
0.010       0.000            1.070          1.025

SRMR (Standardized Root Mean Square Residual)

Mean                                 0.005
Std Dev                              0.003
Number of successful computations      500

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       1.000           -0.003          0.000
0.980       1.000           -0.003          0.000
0.950       1.000           -0.001          0.000
0.900       0.978            0.000          0.001
0.800       0.770            0.002          0.002
0.700       0.642            0.003          0.002
0.500       0.434            0.005          0.004
0.300       0.248            0.006          0.006
0.200       0.170            0.008          0.007
0.100       0.112            0.009          0.009
0.050       0.070            0.010          0.011
0.020       0.038            0.012          0.014
0.010       0.032            0.013          0.015

MODEL RESULTS

ESTIMATES              S. E.     M. S. E.  95%  % Sig
Population   Average   Std. Dev.   Average             Cover Coeff
Y        ON
M                   0.500     0.5007     0.0524     0.0494     0.0027 0.922 1.000
X                   0.200     0.2056     0.0783     0.0784     0.0061 0.938 0.754
Z                   0.100     0.0963     0.0470     0.0433     0.0022 0.926 0.604

M        ON
X                   0.300     0.3010     0.0776     0.0770     0.0060 0.962 0.978
Z                   0.300     0.2999     0.0531     0.0545     0.0028 0.966 1.000
XZ                  0.200     0.2010     0.0775     0.0771     0.0060 0.950 0.744

Intercepts
Y                   0.000    -0.0017     0.0527     0.0522     0.0028 0.934 0.066
M                   0.000    -0.0008     0.0543     0.0545     0.0029 0.946 0.054

Residual Variances
Y                   0.500     0.4938     0.0341     0.0347     0.0012 0.928 1.000
M                   0.500     0.4941     0.0331     0.0346     0.0011 0.950 1.000

INDAVG              0.150     0.1505     0.0417     0.0416     0.0017 0.956 0.974
INDLOW              0.050     0.0497     0.0546     0.0548     0.0030 0.958 0.140
INDHIGH             0.250     0.2514     0.0628     0.0603     0.0039 0.928 0.988

QUALITY OF NUMERICAL RESULTS

Average Condition Number for the Information Matrix      0.798E-03
(ratio of smallest to largest eigenvalue)

TECHNICAL 1 OUTPUT

PARAMETER SPECIFICATION

NU
Y             M             X             Z             XZ
________      ________      ________      ________      ________
1           0             0             0             0             0

LAMBDA
Y             M             X             Z             XZ
________      ________      ________      ________      ________
Y                  0             0             0             0             0
M                  0             0             0             0             0
X                  0             0             0             0             0
Z                  0             0             0             0             0
XZ                 0             0             0             0             0

THETA
Y             M             X             Z             XZ
________      ________      ________      ________      ________
Y                  0
M                  0             0
X                  0             0             0
Z                  0             0             0             0
XZ                 0             0             0             0             0

ALPHA
Y             M             X             Z             XZ
________      ________      ________      ________      ________
1           1             2             0             0             0

BETA
Y             M             X             Z             XZ
________      ________      ________      ________      ________
Y                  0             3             4             5             0
M                  0             0             6             7             8
X                  0             0             0             0             0
Z                  0             0             0             0             0
XZ                 0             0             0             0             0

PSI
Y             M             X             Z             XZ
________      ________      ________      ________      ________
Y                  9
M                  0            10
X                  0             0             0
Z                  0             0             0             0
XZ                 0             0             0             0             0

PARAMETER SPECIFICATION FOR THE ADDITIONAL PARAMETERS

INDAVG        INDLOW        INDHIGH
________      ________      ________
1                 11            12            13

STARTING VALUES

NU
Y             M             X             Z             XZ
________      ________      ________      ________      ________
1         0.000         0.000         0.000         0.000         0.000

LAMBDA
Y             M             X             Z             XZ
________      ________      ________      ________      ________
Y              1.000         0.000         0.000         0.000         0.000
M              0.000         1.000         0.000         0.000         0.000
X              0.000         0.000         1.000         0.000         0.000
Z              0.000         0.000         0.000         1.000         0.000
XZ             0.000         0.000         0.000         0.000         1.000

THETA
Y             M             X             Z             XZ
________      ________      ________      ________      ________
Y              0.000
M              0.000         0.000
X              0.000         0.000         0.000
Z              0.000         0.000         0.000         0.000
XZ             0.000         0.000         0.000         0.000         0.000

ALPHA
Y             M             X             Z             XZ
________      ________      ________      ________      ________
1         0.000         0.000         0.538         0.007         0.237

BETA
Y             M             X             Z             XZ
________      ________      ________      ________      ________
Y              0.000         0.500         0.200         0.100         0.000
M              0.000         0.000         0.300         0.300         0.200
X              0.000         0.000         0.000         0.000         0.000
Z              0.000         0.000         0.000         0.000         0.000
XZ             0.000         0.000         0.000         0.000         0.000

PSI
Y             M             X             Z             XZ
________      ________      ________      ________      ________
Y              0.500
M              0.000         0.500
X              0.000         0.000         0.249
Z              0.000         0.000         0.234         1.054
XZ             0.000         0.000         0.110         0.540         0.485

STARTING VALUES FOR THE ADDITIONAL PARAMETERS

INDAVG        INDLOW        INDHIGH
________      ________      ________
1              0.150         0.050         0.250

DIAGRAM INFORMATION

Mplus diagrams are currently not available for Monte Carlo analysis.
No diagram output was produced.

Beginning Time:  15:02:25
Ending Time:  15:02:28
Elapsed Time:  00:00:03

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