Statistical inference with anchored Bayesian mixture of regressions models: A case study analysis of allometric data

TL;DR

This paper demonstrates how anchored Bayesian mixture of regressions models can improve the analysis of allometric data by using anchor points to address label-switching issues, with a case study on mammalian brain and body mass.

Contribution

It introduces a novel anchored Bayesian mixture of regressions approach that incorporates anchor points to enhance model interpretability and performance in biological data analysis.

Findings

Anchored models outperform standard mixtures in fit and interpretability.

Three anchoring strategies are compared with favorable results.

The approach effectively addresses label-switching in mixture models.

Abstract

We present an illustrative study in which we use a mixture of regressions model to improve on an ill-fitting simple linear regression model relating log brain mass to log body mass for 100 placental mammalian species. The slope of the model is of particular scientific interest because it corresponds to a constant that governs a hypothesized allometric power law relating brain mass to body mass. We model these data using an anchored Bayesian mixture of regressions model, which modifies the standard Bayesian Gaussian mixture by pre-assigning small subsets of observations to given mixture components with probability one. These observations (called anchor points) break the relabeling invariance (or label-switching) typical of exchangeable models. In the article, we develop a strategy for selecting anchor points using tools from case influence diagnostics. We compare the performance of three anchoring methodson the allometric data and in simulated settings.