Boosting functional response models for location, scale and shape with an application to bacterial competition

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 analyse bacterial growth in Escherichia coli in a complex interaction scenario, fruitfully extending usual growth models.