Page 20 - Contributed Paper Session (CPS) - Volume 1

CPS653 Chang-Yun L.

Stochastic search variable selection for definitive
screening designs in split-plot and block
structures
Chang-Yun Lin
Department of Applied Mathematics and Institute of Statistics, National Chung Hsing
University, Taichung, Taiwan

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

1. Introduction
Split-plot definitive screening (SPDS) and block definitive screening (BDS)
designs have been developed for detecting active second-order effects in
screening experiments when split-plot and block structures exist. In the
literature, the multistage regression (MSR) and forward stepwise regression
(FSR) methods were proposed for analyzing data for the two types of designs.
However, there are some limitations and potential problems with the
regression approaches. First, the degrees of freedom may not be large enough
to estimate all active effects. Second, the restricted maximum likelihood
(REML) estimate for the variances of whole-plot and block errors can be zero.
To overcome these problems and to enhance the detection capability, we
propose a stochastic search variable selection (SSVS) method based on the
Bayesian theory. Different from the existing Bayesian approaches for split-plot
and block designs, the proposed SSVS method can perform variable selections
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