Mplus VERSION 7.4
MUTHEN & MUTHEN
06/02/2016 5:21 PM
INPUT INSTRUCTIONS
title:
Pearl (2011) artificial example for n=200
data:
file = n200expanded.txt;
variable:
names = y m x; !x: tx/ctrl, m: mediator, y: outcome
categorical = y m;
usev = y m x mx;
define:
mx=m*x;
analysis:
estimator = ml;
bootstrap = 1000;
model:
y on m x mx;
m on x;
model indirect:
y MOD m mx x;
output:
tech1 tech8 cinterval(bootstrap);
plot:
type = plot3;
INPUT READING TERMINATED NORMALLY
Pearl (2011) artificial example for n=200
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 200
Number of dependent variables 2
Number of independent variables 2
Number of continuous latent variables 0
Observed dependent variables
Binary and ordered categorical (ordinal)
Y M
Observed independent variables
X MX
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 15
Minimum value for logit thresholds -15
Minimum expected cell size for chi-square 0.100D-01
Number of bootstrap draws
Requested 1000
Completed 1000
Optimization algorithm EMA
Integration Specifications
Type STANDARD
Number of integration points 15
Dimensions of numerical integration 0
Adaptive quadrature ON
Link LOGIT
Cholesky OFF
Input data file(s)
n200expanded.txt
Input data format FREE
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
Y
Category 1 0.500 100.000
Category 2 0.500 100.000
M
Category 1 0.425 85.000
Category 2 0.575 115.000
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 6
Loglikelihood
H0 Value -232.709
Information Criteria
Akaike (AIC) 477.418
Bayesian (BIC) 497.208
Sample-Size Adjusted BIC 478.199
(n* = (n + 2) / 24)
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Y ON
M 0.539 0.454 1.188 0.235
X 0.981 0.575 1.707 0.088
MX 1.253 0.753 1.664 0.096
M ON
X 1.568 0.309 5.066 0.000
Thresholds
Y$1 1.163 0.318 3.655 0.000
M$1 0.382 0.200 1.908 0.056
LOGISTIC REGRESSION ODDS RATIO RESULTS
Y ON
M 1.714
X 2.667
MX 3.500
M ON
X 4.795
TOTAL, INDIRECT, AND DIRECT EFFECTS BASED ON COUNTERFACTUALS (CAUSALLY-DEFINED EFFECTS)
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Effects from X to Y
Tot natural IE 0.136 0.050 2.716 0.007
Pure natural DE 0.325 0.082 3.963 0.000
Total effect 0.462 0.063 7.318 0.000
Odds ratios for binary Y
Tot natural IE 1.879 0.436 4.313 0.000
Pure natural DE 3.933 1.784 2.205 0.027
Total effect 7.389 2.782 2.656 0.008
Other effects
Pure natural IE 0.040 0.035 1.148 0.251
Tot natural DE 0.422 0.072 5.843 0.000
Total effect 0.462 0.063 7.318 0.000
Odds ratios for other effects for binary Y
Pure natural IE 1.208 0.199 6.074 0.000
Tot natural DE 6.116 2.509 2.438 0.015
Total effect 7.389 2.782 2.656 0.008
CONFIDENCE INTERVALS OF MODEL RESULTS
Lower .5% Lower 2.5% Lower 5% Estimate Upper 5% Upper 2.5% Upper .5%
Y ON
M -0.584 -0.333 -0.202 0.539 1.300 1.459 1.749
X -0.470 -0.026 0.130 0.981 1.995 2.189 2.603
MX -0.843 -0.352 -0.045 1.253 2.454 2.702 3.134
M ON
X 0.698 0.992 1.075 1.568 2.096 2.187 2.369
Thresholds
Y$1 0.433 0.610 0.693 1.163 1.705 1.833 2.065
M$1 -0.103 0.000 0.056 0.382 0.722 0.783 0.924
CONFIDENCE INTERVALS OF TOTAL, INDIRECT, AND DIRECT EFFECTS BASED ON COUNTERFACTUALS (CAUSALLY-DEFINED EFFECTS)
Lower .5% Lower 2.5% Lower 5% Estimate Upper 5% Upper 2.5% Upper .5%
Effects from X to Y
Tot natural IE 0.023 0.046 0.061 0.136 0.216 0.241 0.285
Pure natural DE 0.112 0.166 0.192 0.325 0.462 0.488 0.543
Total effect 0.293 0.334 0.355 0.462 0.566 0.584 0.616
Odds ratios for binary Y
Tot natural IE 1.117 1.265 1.351 1.879 2.655 2.929 3.406
Pure natural DE 1.589 1.966 2.213 3.933 7.593 8.735 11.504
Total effect 3.382 4.048 4.457 7.389 13.272 14.885 18.378
Other effects
Pure natural IE -0.049 -0.024 -0.014 0.040 0.097 0.112 0.146
Tot natural DE 0.222 0.272 0.300 0.422 0.533 0.559 0.606
Total effect 0.293 0.334 0.355 0.462 0.566 0.584 0.616
Odds ratios for other effects for binary Y
Pure natural IE 0.777 0.888 0.933 1.208 1.568 1.662 1.909
Tot natural DE 2.476 3.129 3.549 6.116 11.117 13.050 16.806
Total effect 3.382 4.048 4.457 7.389 13.272 14.885 18.378
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION
TAU
Y$1 M$1
________ ________
1 5 6
NU
Y M X MX
________ ________ ________ ________
1 0 0 0 0
LAMBDA
Y M X MX
________ ________ ________ ________
Y 0 0 0 0
M 0 0 0 0
X 0 0 0 0
MX 0 0 0 0
THETA
Y M X MX
________ ________ ________ ________
Y 0
M 0 0
X 0 0 0
MX 0 0 0 0
ALPHA
Y M X MX
________ ________ ________ ________
1 0 0 0 0
BETA
Y M X MX
________ ________ ________ ________
Y 0 1 2 3
M 0 0 4 0
X 0 0 0 0
MX 0 0 0 0
PSI
Y M X MX
________ ________ ________ ________
Y 0
M 0 0
X 0 0 0
MX 0 0 0 0
STARTING VALUES
TAU
Y$1 M$1
________ ________
1 0.000 -0.302
NU
Y M X MX
________ ________ ________ ________
1 0.000 0.000 0.000 0.000
LAMBDA
Y M X MX
________ ________ ________ ________
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
MX 0.000 0.000 0.000 1.000
THETA
Y M X MX
________ ________ ________ ________
Y 0.000
M 0.000 0.000
X 0.000 0.000 0.000
MX 0.000 0.000 0.000 0.000
ALPHA
Y M X MX
________ ________ ________ ________
1 0.000 0.000 0.000 0.000
BETA
Y M X MX
________ ________ ________ ________
Y 0.000 0.000 0.000 0.000
M 0.000 0.000 0.000 0.000
X 0.000 0.000 0.000 0.000
MX 0.000 0.000 0.000 0.000
PSI
Y M X MX
________ ________ ________ ________
Y 1.000
M 0.000 1.000
X 0.000 0.000 0.125
MX 0.000 0.000 0.000 0.115
TECHNICAL 8 OUTPUT
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.27500036D+03 0.0000000 0.0000000 EM
2 -0.23328374D+03 41.7166201 0.1516966 EM
3 -0.23271165D+03 0.5720894 0.0024523 EM
4 -0.23270909D+03 0.0025598 0.0000110 EM
5 -0.23270909D+03 0.0000001 0.0000000 EM
PLOT INFORMATION
The following plots are available:
Histograms (sample values)
Scatterplots (sample values)
Sample proportions
Bootstrap distributions
DIAGRAM INFORMATION
Use View Diagram under the Diagram menu in the Mplus Editor to view the diagram.
If running Mplus from the Mplus Diagrammer, the diagram opens automatically.
Diagram output
c:\users\gryphon\desktop\chapter8\ex8.31.dgm
Beginning Time: 17:21:44
Ending Time: 17:21:45
Elapsed Time: 00:00:01
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