Bayes Factors for Comparison of Two-Way ANOVA Models

Abstract

In the traditional two-way analysis of variance (ANOVA) model, it is possible to identify the significance of both the main effects and their interaction based on the P values. However, it is not possible to determine how much data supports the model when these effects are incorporated into the model. To overcome this practical difficulty, we applied Bayes factors for hierarchical models to check the intensity of the effects (both main and interaction). The objective is to identify the impact of the main and interaction effects based on a comparison of Bayes factors of the hierarchical ANOVA models. The application of Bayes factors enables to observe which model strengthens more while including or eliminating the effects in the model. Consequently, this paper proposes three priors such as Zellner's g, Jefferys-Zellner-Siow, and Hyper-g priors, to compute the Bayes factor. Finally, we extended this procedure to the simulation data for the generalization of the Bayesian results.

Keywords

• ANOVA model
• Bayes factor
• Zellner's g prior
• Jeffrey-Zellner-Siow prior
• Hyper-g prior
• Simulation data