Bayesian Variable Selection for Fractional Factorial Experiments with Multilevel Categorical Factors

Abstract

Fractional factorial experiments are an exceedingly important tool to the scientist or engineer working in virtually any sector of industry. As was first demonstrated by Box and Meyer (1993), what has become known as the Bayesian variable-selection approach is a useful addition to the traditional analysis techniques, due to its ability to identify “difficult-to-spot” interaction effects in experiments with complex aliasing. However, the published experiments on which this approach has been applied consist either of two-level factors or factors with quantitative levels. A multilevel categorical factor differs in that its effect must be represented by more than one parameter in the model, these being the regression coefficients associated with a set of dummy variables. Regardless of how the dummy variables are selected, it is not reasonable to assume that these parameters are exchangeable either among themselves or between parameters representing the effect of other factors. Hence, the priors proposed to date cannot be used. We present a simple multivariate normal prior for this effect that is a natural extension of the prior used by previous authors for two-level factors and demonstrate its effectiveness by reanalyzing two multilevel factorial experiments with very complex aliasing.

• Complex Aliasing
• Interactions
• Markov Chain Monte Carlo
• Screening Experiments
• Semiautomatic Priors
• Stochastic Search
• WinBUGS

Additional information

Notes on contributors

Phil Woodward

Mr. Woodward is a Senior Director in Statistics, Pfizer Global R&D. His email address is [email protected].

Rosalind Walley

Miss Walley is a Director in Statistics, Pfizer Global R&D. Her email address is [email protected].