Boosting Functional Response Models for Location, Scale and Shape with an Application to Bacterial Competition

TL;DR

This paper extends GAMLSS to functional responses, enabling detailed modeling of bacterial growth curves with complex covariate effects using gradient boosting, thus improving flexibility and applicability in biological data analysis.

Contribution

The paper introduces a novel extension of GAMLSS for functional responses, incorporating gradient boosting for flexible modeling beyond exponential family distributions.

Findings

Effective modeling of bacterial growth curves.

Enhanced model flexibility with complex covariate effects.

Successful application to E. coli growth data.

Abstract

We extend Generalized Additive Models for Location, Scale, and Shape (GAMLSS) to regression with functional response. This allows us to simultaneously model point-wise mean curves, variances and other distributional parameters of the response in dependence of various scalar and functional covariate effects. In addition, the scope of distributions is extended beyond exponential families. The model is fitted via gradient boosting, which offers inherent model selection and is shown to be suitable for both complex model structures and highly auto-correlated response curves. This enables us to analyze bacterial growth in \textit{Escherichia coli} in a complex interaction scenario, fruitfully extending usual growth models.