CSP 2017 Online Program

Detecting Interaction in Two-Way Unreplicated Experiments via Bayesian Model Selection (303445)

Keywords: interaction effects, latent variables, hidden additivity, non-additivity, Bayesian model selection

The two-way unreplicated layout is frequently used in agriculture, bioinformatics, engineering, manufacturing, medicine, social science, and many other fields. This design is limited in two key ways: first, including the standard set of interaction effects leads to a saturated model that prohibits meaningful inference on parameters; and second, unusual or more complex data relationships may lead to misleading or inaccurate results if the commonly used main effects model is adopted. In this presentation we use Bayesian model selection to compare restricted forms of interaction that allow more flexibility than the main effects model. We illustrate these concepts for a variety of interaction models that have been proposed in the literature and used in practice. We analyze both simulated and real-world data sets to show our methods’ abilities to detect interaction where the main effects model is overly simplistic. Finally, model averaging-based extensions of the selection procedures will be motivated to allow inference on model parameters under the presented non-additive forms.