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

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

model constraint:
new(ind*.15);
ind = b*gamma1;

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                                  2
Number of continuous latent variables                            0

Observed dependent variables

Continuous
Y           M

Observed independent variables
X           Z

Estimator                                                       ML
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
________      ________      ________      ________
1              0.197         0.190         0.500         0.002

Covariances
Y             M             X             Z
________      ________      ________      ________
Y              0.787
M              0.446         0.737
X              0.148         0.155         0.249
Z              0.368         0.460         0.200         0.999

Correlations
Y             M             X             Z
________      ________      ________      ________
Y              1.000
M              0.585         1.000
X              0.335         0.362         1.000
Z              0.415         0.536         0.402         1.000

MODEL FIT INFORMATION

Number of Free Parameters                        9

Loglikelihood

H0 Value

Mean                              -855.918
Std Dev                             19.943
Number of successful computations      500

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.992         -902.311       -901.609
0.980       0.982         -896.875       -895.805
0.950       0.958         -888.722       -888.135
0.900       0.898         -881.477       -882.260
0.800       0.798         -872.702       -873.710
0.700       0.696         -866.376       -866.481
0.500       0.488         -855.918       -856.284
0.300       0.294         -845.460       -845.863
0.200       0.208         -839.135       -838.284
0.100       0.108         -830.360       -828.751
0.050       0.044         -823.115       -823.612
0.020       0.014         -814.962       -818.146
0.010       0.010         -809.526       -812.270

H1 Value

Mean                              -855.918
Std Dev                             19.943
Number of successful computations      500

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.992         -902.311       -901.609
0.980       0.982         -896.875       -895.805
0.950       0.958         -888.722       -888.134
0.900       0.898         -881.477       -882.260
0.800       0.798         -872.702       -873.710
0.700       0.696         -866.376       -866.481
0.500       0.488         -855.918       -856.284
0.300       0.294         -845.460       -845.863
0.200       0.208         -839.135       -838.284
0.100       0.108         -830.360       -828.751
0.050       0.044         -823.115       -823.612
0.020       0.014         -814.962       -818.146
0.010       0.010         -809.526       -812.270

Information Criteria

Akaike (AIC)

Mean                              1729.837
Std Dev                             39.885
Number of successful computations      500

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.990         1637.051       1636.241
0.980       0.986         1647.924       1654.178
0.950       0.956         1664.229       1665.138
0.900       0.892         1678.720       1674.985
0.800       0.792         1696.269       1694.385
0.700       0.706         1708.921       1709.521
0.500       0.512         1729.837       1730.351
0.300       0.304         1750.753       1750.958
0.200       0.202         1763.404       1764.095
0.100       0.102         1780.954       1781.443
0.050       0.042         1795.444       1793.897
0.020       0.018         1811.749       1809.583
0.010       0.008         1822.622       1820.160

Bayesian (BIC)

Mean                              1765.760
Std Dev                             39.885
Number of successful computations      500

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.990         1672.975       1672.164
0.980       0.986         1683.847       1690.102
0.950       0.956         1700.153       1701.061
0.900       0.892         1714.643       1710.908
0.800       0.792         1732.192       1730.309
0.700       0.706         1744.844       1745.445
0.500       0.512         1765.760       1766.274
0.300       0.304         1786.676       1786.881
0.200       0.202         1799.327       1800.018
0.100       0.102         1816.877       1817.366
0.050       0.042         1831.367       1829.820
0.020       0.018         1847.672       1845.506
0.010       0.008         1858.545       1856.083

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

Mean                              1737.202
Std Dev                             39.885
Number of successful computations      500

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.990         1644.417       1643.607
0.980       0.986         1655.290       1661.544
0.950       0.956         1671.595       1672.503
0.900       0.892         1686.085       1682.351
0.800       0.792         1703.635       1701.751
0.700       0.706         1716.286       1716.887
0.500       0.512         1737.202       1737.717
0.300       0.304         1758.118       1758.323
0.200       0.202         1770.770       1771.460
0.100       0.102         1788.319       1788.809
0.050       0.042         1802.810       1801.263
0.020       0.018         1819.115       1816.949
0.010       0.008         1829.988       1827.525

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

CFI/TLI

CFI

Mean                                 1.000
Std Dev                              0.000
Number of successful computations      500

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.982            1.000          1.000
0.980       0.976            1.000          1.000
0.950       0.954            1.000          1.000
0.900       0.900            1.000          1.000
0.800       0.792            1.000          1.000
0.700       0.702            1.000          1.000
0.500       0.514            1.000          1.000
0.300       0.332            1.000          1.000
0.200       0.230            1.000          1.000
0.100       0.094            1.000          1.000
0.050       0.034            1.000          1.000
0.020       0.004            1.000          1.000
0.010       0.002            1.000          1.000

TLI

Mean                                 1.000
Std Dev                              0.000
Number of successful computations      500

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000            1.000          1.000
0.980       0.000            1.000          1.000
0.950       0.000            1.000          1.000
0.900       0.000            1.000          1.000
0.800       0.000            1.000          1.000
0.700       0.000            1.000          1.000
0.500       0.000            1.000          1.000
0.300       0.000            1.000          1.000
0.200       0.000            1.000          1.000
0.100       0.000            1.000          1.000
0.050       0.000            1.000          1.000
0.020       0.000            1.000          1.000
0.010       0.000            1.000          1.000

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       0.998            0.000          0.000
0.950       0.976            0.000          0.000
0.900       0.892            0.000          0.000
0.800       0.744            0.000          0.000
0.700       0.658            0.000          0.000
0.500       0.492            0.000          0.000
0.300       0.328            0.000          0.000
0.200       0.222            0.000          0.000
0.100       0.112            0.000          0.000
0.050       0.044            0.000          0.000
0.020       0.018            0.000          0.000
0.010       0.004            0.000          0.000

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     0.0496     0.0027 0.932 1.000
X                   0.200     0.2056     0.0782     0.0784     0.0061 0.946 0.756
Z                   0.100     0.0963     0.0470     0.0433     0.0022 0.936 0.596

M        ON
X                   0.300     0.3010     0.0788     0.0777     0.0062 0.950 0.972
Z                   0.300     0.4005     0.0390     0.0389     0.0116 0.272 1.000

Intercepts
Y                   0.000    -0.0017     0.0527     0.0522     0.0028 0.934 0.066
M                   0.000     0.0393     0.0530     0.0526     0.0043 0.882 0.118

Residual Variances
Y                   0.500     0.4938     0.0341     0.0349     0.0012 0.932 1.000
M                   0.500     0.5037     0.0344     0.0356     0.0012 0.954 1.000

IND                 0.150     0.1506     0.0423     0.0419     0.0018 0.958 0.970

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
________      ________      ________      ________
1           0             0             0             0

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

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

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

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

PSI
Y             M             X             Z
________      ________      ________      ________
Y                  8
M                  0             9
X                  0             0             0
Z                  0             0             0             0

PARAMETER SPECIFICATION FOR THE ADDITIONAL PARAMETERS

IND
________
1                 10

STARTING VALUES

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

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

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

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

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

PSI
Y             M             X             Z
________      ________      ________      ________
Y              0.500
M              0.000         0.500
X              0.000         0.000         0.249
Z              0.000         0.000         0.234         1.054

STARTING VALUES FOR THE ADDITIONAL PARAMETERS

IND
________
1              0.150

DIAGRAM INFORMATION

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

Beginning Time:  15:03:33
Ending Time:  15:03:36
Elapsed Time:  00:00:03

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Los Angeles, CA  90066

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