Mplus DEVELOPMENT (Mpdev 6/1/2016)
MUTHEN & MUTHEN
06/03/2016 7:21 AM
INPUT INSTRUCTIONS
title:
Simulating binary X, cont latent M, binary Y
Step 2
data:
file = n200Perc20replist.dat;
type = montecarlo;
variable:
names = y m1-m3 x;
usev = y x sum;
categorical = y;
define:
sum = sum(m1-m3);
analysis:
estimator = ml;
link = probit;
model:
y on x*-.2
sum*-.25;
[y$1*.75];
sum on x*.7; !R-square 0.10
model indirect:
y IND sum x;
INPUT READING TERMINATED NORMALLY
Simulating binary X, cont latent M, binary Y
Step 2
SUMMARY OF ANALYSIS
Number of groups 1
Average number of observations 200
Number of replications
Requested 500
Completed 500
Number of dependent variables 2
Number of independent variables 1
Number of continuous latent variables 0
Observed dependent variables
Continuous
SUM
Binary and ordered categorical (ordinal)
Y
Observed independent variables
X
Estimator ML
Information matrix OBSERVED
Optimization Specifications for the Quasi-Newton Algorithm for
Continuous Outcomes
Maximum number of iterations 100
Convergence criterion 0.100D-05
Optimization Specifications for the EM Algorithm
Maximum number of iterations 500
Convergence criteria
Loglikelihood change 0.100D-02
Relative loglikelihood change 0.100D-05
Derivative 0.100D-02
Optimization Specifications for the M step of the EM Algorithm for
Categorical Latent variables
Number of M step iterations 1
M step convergence criterion 0.100D-02
Basis for M step termination ITERATION
Optimization Specifications for the M step of the EM Algorithm for
Censored, Binary or Ordered Categorical (Ordinal), Unordered
Categorical (Nominal) and Count Outcomes
Number of M step iterations 1
M step convergence criterion 0.100D-02
Basis for M step termination ITERATION
Maximum value for logit thresholds 10
Minimum value for logit thresholds -10
Minimum expected cell size for chi-square 0.100D-01
Optimization algorithm EMA
Integration Specifications
Type STANDARD
Number of integration points 15
Dimensions of numerical integration 0
Adaptive quadrature ON
Link PROBIT
Cholesky ON
Input data file(s)
Multiple data files from
n200Perc20replist.dat
Input data format FREE
UNIVARIATE PROPORTIONS FOR CATEGORICAL VARIABLES FOR THE FIRST REPLICATION
Y
Category 1 0.780
Category 2 0.220
SAMPLE STATISTICS
NOTE: These are average results over 500 data sets.
SAMPLE STATISTICS
Means
SUM X
________ ________
1 1.047 0.500
Covariances
SUM X
________ ________
SUM 12.119
X 0.526 0.249
Correlations
SUM X
________ ________
SUM 1.000
X 0.303 1.000
MODEL FIT INFORMATION
Number of Free Parameters 6
Loglikelihood
H0 Value
Mean -575.745
Std Dev 12.210
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.994 -604.149 -602.979
0.980 0.980 -600.820 -601.081
0.950 0.956 -595.829 -595.352
0.900 0.894 -591.393 -591.866
0.800 0.786 -586.021 -586.719
0.700 0.700 -582.148 -582.378
0.500 0.500 -575.745 -575.795
0.300 0.306 -569.343 -569.221
0.200 0.194 -565.470 -565.782
0.100 0.096 -560.098 -560.393
0.050 0.050 -555.662 -555.758
0.020 0.020 -550.671 -551.170
0.010 0.014 -547.342 -546.022
Information Criteria
Akaike (AIC)
Mean 1163.491
Std Dev 24.419
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.986 1106.685 1104.020
0.980 0.980 1113.341 1113.039
0.950 0.950 1123.324 1122.505
0.900 0.904 1132.195 1132.415
0.800 0.806 1142.940 1143.463
0.700 0.694 1150.685 1150.429
0.500 0.500 1163.491 1163.419
0.300 0.300 1176.296 1176.245
0.200 0.214 1184.042 1185.074
0.100 0.106 1194.786 1195.357
0.050 0.044 1203.658 1202.687
0.020 0.020 1213.640 1212.179
0.010 0.006 1220.297 1217.582
Bayesian (BIC)
Mean 1183.281
Std Dev 24.419
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.986 1126.474 1123.810
0.980 0.980 1133.131 1132.829
0.950 0.950 1143.114 1142.295
0.900 0.904 1151.985 1152.205
0.800 0.806 1162.730 1163.253
0.700 0.694 1170.475 1170.219
0.500 0.500 1183.281 1183.209
0.300 0.300 1196.086 1196.035
0.200 0.214 1203.832 1204.864
0.100 0.106 1214.576 1215.147
0.050 0.044 1223.448 1222.477
0.020 0.020 1233.430 1231.968
0.010 0.006 1240.087 1237.372
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 1164.272
Std Dev 24.419
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.986 1107.466 1104.802
0.980 0.980 1114.122 1113.820
0.950 0.950 1124.105 1123.286
0.900 0.904 1132.977 1133.196
0.800 0.806 1143.721 1144.245
0.700 0.694 1151.467 1151.210
0.500 0.500 1164.272 1164.200
0.300 0.300 1177.078 1177.026
0.200 0.214 1184.823 1185.855
0.100 0.106 1195.568 1196.138
0.050 0.044 1204.439 1203.468
0.020 0.020 1214.422 1212.960
0.010 0.006 1221.078 1218.364
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Y ON
X -0.200 -0.9320 0.3218 0.3083 0.6393 0.328 0.892
SUM -0.250 -0.4858 0.0794 0.0751 0.0619 0.022 1.000
SUM ON
X 0.700 2.1155 0.4715 0.4684 2.2256 0.148 0.996
Intercepts
SUM 1.247 -0.0102 0.3305 0.3311 1.6900 0.034 0.064
Thresholds
Y$1 0.750 0.5279 0.1918 0.1791 0.0860 0.712 0.870
Residual Variances
SUM 0.500 10.9482 1.1407 1.0947 110.4639 0.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.155E-01
(ratio of smallest to largest eigenvalue)
TOTAL, TOTAL INDIRECT, SPECIFIC INDIRECT, AND DIRECT EFFECTS FOR LATENT RESPONSE VARIABLES
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Effects from X to Y
Indirect -0.175 -1.0299 0.2937 0.2796 0.8170 0.066 0.996
Direct effect -0.200 -0.9320 0.3218 0.3083 0.6393 0.328 0.892
TOTAL, INDIRECT, AND DIRECT EFFECTS BASED ON COUNTERFACTUALS (CAUSALLY-DEFINED EFFECTS)
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Effects from X to Y
Tot natural IE -0.028 -0.1254 0.0353 0.0347 0.0106 0.140 0.994
Pure natural DE -0.041 -0.1689 0.0550 0.0534 0.0194 0.338 0.898
Total effect -0.069 -0.2943 0.0548 0.0543 0.0536 0.024 0.998
Odds ratios for binary Y
Tot natural IE 0.711 0.3798 0.0886 0.0875 0.1177 0.098 1.000
Pure natural DE 0.691 0.4556 0.1296 0.1250 0.0720 0.506 0.996
Total effect 0.491 0.1739 0.0673 0.0641 0.1052 0.048 0.978
Other effects
Pure natural IE -0.036 -0.1829 0.0419 0.0421 0.0233 0.056 0.996
Tot natural DE -0.033 -0.1114 0.0375 0.0363 0.0075 0.422 0.888
Total effect -0.069 -0.2943 0.0548 0.0543 0.0536 0.024 0.998
Odds ratios for other effects for binary Y
Pure natural IE 0.724 0.4147 0.0869 0.0861 0.1032 0.128 1.000
Tot natural DE 0.678 0.4196 0.1334 0.1287 0.0848 0.436 0.992
Total effect 0.491 0.1739 0.0673 0.0641 0.1052 0.048 0.978
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION
TAU
Y$1
________
1 6
NU
Y SUM X
________ ________ ________
1 0 0 0
LAMBDA
Y SUM X
________ ________ ________
Y 0 0 0
SUM 0 0 0
X 0 0 0
THETA
Y SUM X
________ ________ ________
Y 0
SUM 0 0
X 0 0 0
ALPHA
Y SUM X
________ ________ ________
1 0 1 0
BETA
Y SUM X
________ ________ ________
Y 0 2 3
SUM 0 0 4
X 0 0 0
PSI
Y SUM X
________ ________ ________
Y 0
SUM 0 5
X 0 0 0
STARTING VALUES
TAU
Y$1
________
1 0.750
NU
Y SUM X
________ ________ ________
1 0.000 0.000 0.000
LAMBDA
Y SUM X
________ ________ ________
Y 1.000 0.000 0.000
SUM 0.000 1.000 0.000
X 0.000 0.000 1.000
THETA
Y SUM X
________ ________ ________
Y 0.000
SUM 0.000 0.000
X 0.000 0.000 0.000
ALPHA
Y SUM X
________ ________ ________
1 0.000 1.247 0.000
BETA
Y SUM X
________ ________ ________
Y 0.000 -0.250 -0.200
SUM 0.000 0.000 0.700
X 0.000 0.000 0.000
PSI
Y SUM X
________ ________ ________
Y 1.000
SUM 0.000 0.500
X 0.000 0.000 0.500
Beginning Time: 07:21:58
Ending Time: 07:22:08
Elapsed Time: 00:00:10
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