Bayesian Analysis of Two-Level Fractional Factorial Experiments with Non-Normal Responses

An intractable issue on screening experiments is to identify significant effects and to select the best model when the number of factors is large, especially for fractional factorial experiments with non-normal responses. In such cases, a three-stage Bayesian approach based on generalized linear models (GLMs) is proposed to identify which effects should be included in the target model where the principles of effect sparsity, hierarchy, and heredity are successfully considered. Three simulation experiments with non-normal responses which follow Poisson, binomial, and gamma distributions are presented to illustrate the performance of the proposed approach.