On the detectability of different forms of interaction in regression models

TL;DR

This paper derives an asymptotic power function for likelihood-based tests to detect various interaction forms in regression models, comparing pairwise and diffuse interaction models to assess their detectability.

Contribution

It introduces a general framework for evaluating the power of tests for different interaction types, including under model misspecification, and contrasts pairwise with diffuse interaction models.

Findings

Likelihood-based tests have varying power depending on interaction type.

Diffuse interaction models are generally harder to detect than pairwise interactions.

The asymptotic power function aids in understanding interaction detectability under misspecification.

Abstract

We derive an asymptotic power function for a likelihood-based test for interaction in a regression model, with possibly misspecified alternative distribution. This allows a general investigation of types of interactions which are poorly or well detected via data. Principally we contrast pairwise-interaction models with `diffuse interaction models' as introduced in Gustafson, Kazi, and Levy (2005).