Regression Models for Order-of-Addition Experiments

TL;DR

This paper reviews existing regression models for order-of-addition experiments and introduces a new response surface regression approach, demonstrating its competitiveness and advocating model averaging for improved analysis.

Contribution

It proposes a novel response surface regression model for order-of-addition experiments and integrates model averaging with a compound optimality criterion.

Findings

RS models are competitive with traditional methods

Model averaging improves analysis robustness

Design approach with compound optimality criterion is effective

Abstract

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. Such experiments may be analysed 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.