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Abstract:
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Two-way factorial layouts are ubiquitous in medicine, bioinformatics, and many other disciplines. These designs are popular when replication is expensive, impractical, or impossible. However, lack of replication imposes severe restrictions on the extent to which interaction effects can be studied, as the full interaction model is saturated in this setting. Hidden additivity is an intuitive, latent group-based form of interaction that allows for statistical inference to proceed. To date, detection of hidden additivity and other restricted forms of interaction have been approached largely using hypothesis testing from the classical perspective. Bayesian model selection provides another philosophically pleasing approach for this problem. In this talk I will describe approaches to detect hidden additivity and other non-additive forms using Bayesian model selection. These methods will be compared and contrasted with the classical approach and illustrated using multiple real world data sets.
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