Joint Identification of Location and Dispersion Effects in Unreplicated Two-Level Factorials

Andrew J Henrey,Thomas M Loughin

doi:10.1080/00401706.2015.1114024

Abstract

Most procedures that have been proposed to identify dispersion effects in unreplicated factorial designs assume that location effects have been identified correctly. Incorrect identification of location effects may impair subsequent identification of dispersion effects. We develop a method for joint identification of location and dispersion effects that can reliably identify active effects of both types. A normal-based model containing parameters for effects in both the mean and variance is used. Parameters are estimated using maximum likelihood, and subsequent effect selection is done using a specially derived information criterion. An exhaustive search through a limited version of the space of possible models is conducted. Both a single-model output and model averaging are considered. The method is shown to be capable of identifying sensible location-dispersion models that are missed by methods that rely on sequential estimation of location and dispersion effects. Supplementary materials for this article are available online.

Highlights

In many research and quality-improvement endeavors, experiments are run using unreplicated full or fractional factorial designs at 2 levels per factor
In this paper we have developed the first fully automated analysis procedure for 2k factorial designs that can identify both location and dispersion effects in a single step
The Harvey test assumes a normal distribution with loglinear dispersion effects, which is the same model that was used for the simulations

Summary

Introduction

In many research and quality-improvement endeavors, experiments are run using unreplicated full or fractional factorial designs at 2 levels per factor (generically referred to here as 2k designs, where k is the number of factors; see Wu and Hamada 2000). These experiments are generally intended to identify factorial effects that influence the mean response. Box and Meyer (1986) developed a seminal procedure to test for “dispersion effects” in data from a 2k experiment using residuals from a given location model. For a nice review of these procedures see Bursztyn and Steinberg (2006)

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