Regression models for order-of-addition experiments.

Hans‐Peter Piepho,Emlyn R Williams

doi:10.1002/bimj.202100048

Abstract

The purpose of order-of-addition (OofA) experiments is to identify the best order in a sequence of m components in a system. Such experiments may be analyzed by various regression models, the most popular ones being based on pairwise ordering (PWO) factors or on component-position (CP) factors. This paper reviews these models and extensions and proposes a new class of models based on response surface (RS) regression using component position numbers as predictor variables. Using two published examples, it is shown that RS models can be quite competitive. In case of model uncertainty, we advocate the use of model averaging for analysis. The averaging idea leads naturally to a design approach based on a compound optimality criterion assigning weights to each candidate model.

Highlights

The purpose of order-of-addition (OofA) experiments is to identify the best order in a sequence of m components in a system or treatment (Van Nostrand 1995)
M herbicides may need to be combined to obtain a herbicide mixture targeting a range of weed species and it is not clear in which order the mixture components should be added to the tank (Mee 2020)
Both the pairwise ordering (PWO) and the CP model imply that the position of a component in the sequence matters, but they differ in how position is thought to affect the outcome

Summary

Introduction

The purpose of order-of-addition (OofA) experiments is to identify the best order in a sequence of m components in a system or treatment (Van Nostrand 1995). M herbicides may need to be combined to obtain a herbicide mixture targeting a range of weed species and it is not clear in which order the mixture components should be added to the tank (Mee 2020) Another example is a medical treatment involving m drugs, and the optimal order of administration needs to be determined (Table 1; Yang et al 2020). We may set for j m or c m (baseline constraints) Both the PWO and the CP model imply that the position of a component in the sequence matters, but they differ in how position is thought to affect the outcome. We will consider the implications for design

Regression models

Criteria for judging the predictive accuracy of a model for a given design

Model averaging

Examples

Discussion