Order-of-Addition Modeling

Abstract

Since Van Nostrand (1995), the literature on order of addition experiments has generally relied on main effects models constructed from pair-wise ordering (PWO) factors.This article constructs models utilizing interactions of PWO factors to explain variation that is best accounted for by the ordering of sets of three or more components.Order-of-addition orthogonal arrays, as defined by Voelkel (2018), are optimal for fitting the main effects PWO model, but they differ in terms of their susceptibility to bias due to model misspecification.A measure computed from the alias matrix is proposed to identify robust PWO designs, and illustrated for cases with four and five components.Consideration of applications with constraints on the ordering, as well order of addition experiments having additional mixture proportion and factorial factors, are discussed briefly.Two drug sequence experiments obtained by private consulting are used to contrast the usefulness of different order of addition models.

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