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Abstract:
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The two-way unreplicated factorial layout is a common, economical study design. While the full complement of standard interaction effects are unavailable for inference when replication is absent, many restricted forms of interaction have been proposed. To date, most work in this area focuses on accept/reject decisions with respect to restricted forms of interaction. In this talk, we describe a Bayesian model averaging-based approach to perform inference on cell means and error variance for this class of designs. Hidden additivity, a recent and intuitive form of interaction, is used to accommodate non-additive effects. The approach is fully Bayesian and uses the Zellner-Siow formulation of the mixture g-prior. The method is illustrated on two empirical data sets and simulated data, and the method is compared with a regularization-based approach. The study concludes that Bayesian model selection is a fruitful approach to detect hidden additivity, and model averaging allows for inference on quantities of interest under model uncertainty with respect to interaction effects.
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