Interaction effects in pairwise ordering model

Abstract

In an order-of-addition (OofA) experiment, the response is a function of the addition order of components. The key objective of the OofA experiments is to find the optimal order of addition. The most popularly used model for OofA experiments is perhaps the pairwise ordering (PWO) model, which assumes that the response can be fully accounted by the pairwise ordering of components. Recently, the PWO model has been extended by adding the interactions of PWO factors, to account for variations caused by the ordering of sets of three or more components, where the interaction term is defined by the multiplication of two PWO factors. This paper introduces a novel class of conditional PWO effect to study the interaction effect between PWO factors. The advantages of the proposed interaction terms are studied. Based on these conditional effects, a new model is proposed. The optimal order of addition can be straightforwardly obtained via the proposed model.

Keywords:

• conditional effect
• interaction effect
• order-of-addition experiment
• pairwise ordering model

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

The authors confirm that the data supporting the findings of this study are available within the article and its supplementary materials.

Additional information

Funding

Chunyan Wang is supported by the National Natural Science Foundation of China (Grant No. 12131001). Dennis K. J. Lin is supported by the National Science Foundation of USA (Grant No. DMS-18102925).

Notes on contributors

Chunyan Wang

Dr. Wang is a Lecturer of Center for Applied Statistics and School of Statistics, Renmin University of China. Her email address is [email protected].

Dennis K. J. Lin

Dr. Lin is a Distinguished Professor and Head in the Department of Statistics at Purdue University. He is a fellow of ASQ (also fellows of IMS, RSS, ISI, and ASA). His email address is [email protected].