A Coefficient of Determination (R2) for Linear Mixed Models

TL;DR

This paper introduces a new, universally applicable R2 measure for linear mixed models, addressing the challenge of quantifying goodness of fit in models with heteroscedasticity and random effects, with biological applications.

Contribution

It proposes a novel R2 measure for linear mixed models that accounts for heteroscedasticity and covariance, filling a gap in model assessment tools.

Findings

The new R2 measure is applicable across various biological data analyses.

It effectively accounts for heteroscedasticity and random effects.

Demonstrated through three biological case studies.

Abstract

Extensions of linear models are very commonly used in the analysis of biological data. Whereas goodness of fit measures such as the coefficient of determination (R2) or the adjusted R2 are well established for linear models, it is not obvious how such measures should be defined for generalized linear and mixed models. There are by now several proposals but no consensus has yet emerged as to the best unified approach in these settings. In particular, it is an open question how to best account for heteroscedasticity and for covariance among observations induced by random effects. This paper proposes a new approach that addresses this issue and is universally applicable. It is exemplified using three biological examples.