The Impact of Model Assumptions in Scalar-on-Image Regression

TL;DR

This paper systematically reviews scalar-on-image regression models, focusing on their assumptions, and demonstrates how these assumptions significantly affect estimates and interpretability through simulations and neuroimaging data applications.

Contribution

It categorizes model assumptions, develops measures to assess their validity, and provides practical recommendations for modeling and interpretation in scalar-on-image regression.

Findings

Different assumptions lead to substantially different estimates.

Model assumptions influence interpretability despite similar predictive performance.

Proposed measures help evaluate assumption validity in practice.

Abstract

Complex statistical models such as scalar-on-image regression often require strong assumptions to overcome the issue of non-identifiability. While in theory it is well understood that model assumptions can strongly influence the results, this seems to be underappreciated, or played down, in practice. The article gives a systematic overview of the main approaches for scalar-on-image regression with a special focus on their assumptions. We categorize the assumptions and develop measures to quantify the degree to which they are met. The impact of model assumptions and the practical usage of the proposed measures are illustrated in a simulation study and in an application to neuroimaging data. The results show that different assumptions indeed lead to quite different estimates with similar predictive ability, raising the question of their interpretability. We give recommendations for making modeling and interpretation decisions in practice, based on the new measures and simulations using hypothetic coefficient images and the observed data.