Stochastic search variable selection for split-plot and blocked screening designs

Abstract

Split-plot definitive screening and blocked definitive screening designs have been developed for detecting active main effects and second-order effects in screening experiments when split-plot and block structures exist. In the literature, multistage regression and forward stepwise regression methods were proposed for data analysis on the two types of designs. However, classical regression approaches present limitations and potential problems. First, the degrees of freedom may not be large enough to estimate all active effects. Second, the restricted maximum-likelihood estimates for variances of whole-plot and block errors can be zero. To solve these problems and enhance detection capability, we propose a stochastic search variable selection (SSVS) method based on Bayesian theory. Different from the existing Bayesian approaches for split-plot and blocked designs, the proposed SSVS method can perform variable selections and choose models that follow the effect heredity principle. Markov chain Monte Carlo and Gibbs sampling are applied and a general WinBUGS code, which can be used for any split-plot and blocked screening design, is provided. Simulation studies are conducted and their results show that the proposed SSVS method effectively controls the false discovery rate and has higher detection capability than the two regression methods.