Objective Bayesian Comparison of Constrained Analysis of Variance Models

Objective Bayesian Comparison of Constrained Analysis of Variance Models In the social sciences we are often interested in comparing models specified by parametric equality or inequality constraints. For instance, when examining three group means $$\{ \mu _1, \mu _2, \mu _3\}$$ { μ 1 , μ 2 , μ 3 } through an analysis of variance (ANOVA), a model may specify that $$\mu _1<\mu _2<\mu _3$$ μ 1 < μ 2 < μ 3 , while another one may state that $$\{ \mu _1=\mu _3\} <\mu _2$$ { μ 1 = μ 3 } < μ 2 , and finally a third model may instead suggest that all means are unrestricted. This is a challenging problem, because it involves a combination of nonnested models, as well as nested models having the same dimension. We adopt an objective Bayesian approach, requiring no prior specification from the user, and derive the posterior probability of each model under consideration. Our method is based on the intrinsic prior methodology, suitably modified to accommodate equality and inequality constraints. Focussing on normal ANOVA models, a comparative assessment is carried out through simulation studies. We also present an application to real data collected in a psychological experiment. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Psychometrika Springer Journals

Objective Bayesian Comparison of Constrained Analysis of Variance Models

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Publisher
Springer US
Copyright
Copyright © 2016 by The Psychometric Society
Subject
Psychology; Psychometrics; Assessment, Testing and Evaluation; Statistics for Social Science, Behavorial Science, Education, Public Policy, and Law; Statistical Theory and Methods
ISSN
0033-3123
eISSN
1860-0980
D.O.I.
10.1007/s11336-016-9516-y
Publisher site
See Article on Publisher Site

Abstract

In the social sciences we are often interested in comparing models specified by parametric equality or inequality constraints. For instance, when examining three group means $$\{ \mu _1, \mu _2, \mu _3\}$$ { μ 1 , μ 2 , μ 3 } through an analysis of variance (ANOVA), a model may specify that $$\mu _1<\mu _2<\mu _3$$ μ 1 < μ 2 < μ 3 , while another one may state that $$\{ \mu _1=\mu _3\} <\mu _2$$ { μ 1 = μ 3 } < μ 2 , and finally a third model may instead suggest that all means are unrestricted. This is a challenging problem, because it involves a combination of nonnested models, as well as nested models having the same dimension. We adopt an objective Bayesian approach, requiring no prior specification from the user, and derive the posterior probability of each model under consideration. Our method is based on the intrinsic prior methodology, suitably modified to accommodate equality and inequality constraints. Focussing on normal ANOVA models, a comparative assessment is carried out through simulation studies. We also present an application to real data collected in a psychological experiment.

Journal

PsychometrikaSpringer Journals

Published: Oct 4, 2016

References

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