ENBIS: European Network for Business and Industrial Statistics

Bayesian variable selection with effect heredity principle

21 September 2009, 15:05 – 15:25

Abstract

Submitted by

Hidehisa Noguchi

Authors

Hidehisa Noguchi Yoshikazu Ojima Seiichi Yasui

Affiliation

Tokyo University of Science

Abstract

In design of experiments, screening factors are supposed to have active effect. To identify the factors is important in practical experimental design. So selection predictor is useful method. Whereas procedures like forward selection, backward elimination, or stepwise regression can be easily used. There is a Bayesian variable selection in which a prior probability is assigned for each considered model and then a model with the highest posterior probability given the data is identified through Gibbs sampling.
Bayesian variable selection can be more flexible and powerful by introducing hierarchical priors that incorporates the effect heredity principle.
By using this method, effect heredity principle can be introduced in the algorithm but it needs to be divided into several delicate principles, such as strong heredity and weak heredity, conditional on a nature of interaction.
For example, interaction AB can be divided into several types.
(1) Main effects A and B are included in model also and interaction AB is included.
(2) Main effect A or B and interaction AB are included in the model.
(3) Neither A nor B is included in model, but the interaction AB is included.
In this case, (1) corresponds to strong heredity principle and (2) and (3) corresponds to a kind of weak heredity principles.
In this method, the probability of these types must be set discretely under implicit ordering; (1) is larger or equal to (2) and (2) is larger or equal to (3).
This paper provides a comprehensive methodology for effect heredity principle based on a Bayesian variable selection algorithm.
By assuming a distribution to this implicit ordering, the set probabilities are calculated.
The proposed methodology is demonstrated with the design in which a main effect isn’t either orthogonal to or completely aliased with an interaction, like non-geometric Plackett-Burman designs.

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