Mplus VERSION 7.4
MUTHEN & MUTHEN
06/02/2016 5:16 PM
INPUT INSTRUCTIONS
title:
hypothetical potential outcome example data
data:
file = potential.txt;
variable:
names = x m y;
usev = x m y mx;
categorical = m;
define:
mx = m*x;
analysis:
estimator = mlr;
model:
y on m x mx;
m on x;
model indirect:
y mod m mx x;
output:
sampstat tech1 tech8 cinterval;
INPUT READING TERMINATED NORMALLY
hypothetical potential outcome example data
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 6
Number of dependent variables 2
Number of independent variables 2
Number of continuous latent variables 0
Observed dependent variables
Continuous
Y
Binary and ordered categorical (ordinal)
M
Observed independent variables
X MX
Estimator MLR
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
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)
potential.txt
Input data format FREE
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
M
Category 1 0.500 3.000
Category 2 0.500 3.000
SAMPLE STATISTICS
SAMPLE STATISTICS
Means
Y X MX
________ ________ ________
1 10.167 0.500 0.333
Covariances
Y X MX
________ ________ ________
Y 7.806
X 0.583 0.250
MX 0.778 0.167 0.222
Correlations
Y X MX
________ ________ ________
Y 1.000
X 0.418 1.000
MX 0.591 0.707 1.000
UNIVARIATE SAMPLE STATISTICS
UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS
Variable/ Mean/ Skewness/ Minimum/ % with Percentiles
Sample Size Variance Kurtosis Maximum Min/Max 20%/60% 40%/80% Median
Y 10.167 -0.584 5.000 16.67% 5.000 9.000 10.500
6.000 7.806 -0.423 14.000 16.67% 11.000 12.000
X 0.500 0.000 0.000 50.00% 0.000 0.000 0.500
6.000 0.250 -2.000 1.000 50.00% 1.000 1.000
MX 0.333 0.707 0.000 66.67% 0.000 0.000 0.000
6.000 0.222 -1.500 1.000 33.33% 0.000 1.000
THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE
TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NON-POSITIVE DEFINITE
FIRST-ORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING
VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE
CONDITION NUMBER IS 0.259D-15. PROBLEM INVOLVING THE FOLLOWING PARAMETER:
Parameter 4, Y ON X
NOTE THAT THE NUMBER OF PARAMETERS IS GREATER THAN THE SAMPLE SIZE.
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 7
Loglikelihood
H0 Value -17.059
H0 Scaling Correction Factor 0.8010
for MLR
Information Criteria
Akaike (AIC) 48.119
Bayesian (BIC) 46.661
Sample-Size Adjusted BIC 26.428
(n* = (n + 2) / 24)
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Y ON
M 1.500 2.475 0.606 0.544
X 0.500 2.475 0.202 0.840
MX 2.000 2.693 0.743 0.458
M ON
X 1.386 1.732 0.800 0.423
Intercepts
Y 8.500 2.475 3.435 0.001
Thresholds
M$1 0.693 1.225 0.566 0.571
Residual Variances
Y 4.833 2.174 2.224 0.026
LOGISTIC REGRESSION ODDS RATIO RESULTS
M ON
X 4.000
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.259E-15
(ratio of smallest to largest eigenvalue)
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 1.167 1.393 0.838 0.402
Pure natural DE 1.167 1.773 0.658 0.511
Total effect 2.333 2.073 1.126 0.260
Other effects
Pure natural IE 0.500 1.007 0.497 0.619
Tot natural DE 1.833 1.215 1.509 0.131
Total effect 2.333 2.073 1.126 0.260
CONFIDENCE INTERVALS OF MODEL RESULTS
Lower .5% Lower 2.5% Lower 5% Estimate Upper 5% Upper 2.5% Upper .5%
Y ON
M -4.875 -3.351 -2.571 1.500 5.571 6.351 7.875
X -5.875 -4.351 -3.571 0.500 4.571 5.351 6.875
MX -4.936 -3.277 -2.429 2.000 6.429 7.277 8.936
M ON
X -3.075 -2.009 -1.463 1.386 4.236 4.781 5.848
Intercepts
Y 2.125 3.649 4.429 8.500 12.571 13.351 14.875
Thresholds
M$1 -2.462 -1.707 -1.322 0.693 2.708 3.094 3.848
Residual Variances
Y -0.765 0.573 1.258 4.833 8.409 9.094 10.432
CONFIDENCE INTERVALS FOR THE LOGISTIC REGRESSION ODDS RATIO RESULTS
M ON
X 0.046 0.134 0.232 4.000 69.097 119.237 346.440
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 -2.421 -1.563 -1.124 1.167 3.458 3.896 4.754
Pure natural DE -3.400 -2.308 -1.750 1.167 4.083 4.642 5.734
Total effect -3.006 -1.729 -1.076 2.333 5.743 6.396 7.672
Other effects
Pure natural IE -2.094 -1.474 -1.156 0.500 2.156 2.474 3.094
Tot natural DE -1.297 -0.549 -0.166 1.833 3.832 4.215 4.964
Total effect -3.006 -1.729 -1.076 2.333 5.743 6.396 7.672
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION
TAU
M$1
________
1 7
NU
M Y X MX
________ ________ ________ ________
1 0 0 0 0
LAMBDA
M Y X MX
________ ________ ________ ________
M 0 0 0 0
Y 0 0 0 0
X 0 0 0 0
MX 0 0 0 0
THETA
M Y X MX
________ ________ ________ ________
M 0
Y 0 0
X 0 0 0
MX 0 0 0 0
ALPHA
M Y X MX
________ ________ ________ ________
1 0 1 0 0
BETA
M Y X MX
________ ________ ________ ________
M 0 0 2 0
Y 3 0 4 5
X 0 0 0 0
MX 0 0 0 0
PSI
M Y X MX
________ ________ ________ ________
M 0
Y 0 6
X 0 0 0
MX 0 0 0 0
STARTING VALUES
TAU
M$1
________
1 0.000
NU
M Y X MX
________ ________ ________ ________
1 0.000 0.000 0.000 0.000
LAMBDA
M Y X MX
________ ________ ________ ________
M 1.000 0.000 0.000 0.000
Y 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
M Y X MX
________ ________ ________ ________
M 0.000
Y 0.000 0.000
X 0.000 0.000 0.000
MX 0.000 0.000 0.000 0.000
ALPHA
M Y X MX
________ ________ ________ ________
1 0.000 10.167 0.000 0.000
BETA
M Y X MX
________ ________ ________ ________
M 0.000 0.000 0.000 0.000
Y 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
M Y X MX
________ ________ ________ ________
M 1.000
Y 0.000 3.903
X 0.000 0.000 0.125
MX 0.000 0.000 0.000 0.111
TECHNICAL 8 OUTPUT
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.19757580D+02 0.0000000 0.0000000 EM
2 -0.17059794D+02 2.6977859 0.1365443 EM
3 -0.17059325D+02 0.0004688 0.0000275 EM
4 -0.17059325D+02 0.0000000 0.0000000 EM
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\ex8.22.dgm
Beginning Time: 17:16:53
Ending Time: 17:16:53
Elapsed Time: 00:00:00
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