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.

Additive Density-on-Scalar Regression in Bayes Hilbert Spaces with an Application to Gender Economics

“…More details about how to include this constraint in a functional linear array model for function-on-scalar regression can be found in appendix A of . A similar procedure can be used to obtain a centering of interaction effects around the main effects, see appendix A of Stöcker et al (2021). Both approaches are based on Wood (2017, Section 1.8.1) and can be transferred straightforwardly to density-on-scalar regression.…”

Comments on: Inference and computation with Generalized Additive Models and their extensions

“…Each partial effect h j can depend on one or several scalar and/or functional covariates x i and vary with t id . This can also be generalized to some other feature than the mean, like, e.g., the mean composed with a link function (Scheipl et al 2016), a quantile (Brockhaus et al 2015), or even several features like the mean and variance (Brockhaus et al 2018;Stöcker et al 2018). As covariate effects are unlikely to explain all structure in the data and there will thus be remaining auto-correlation along t, it is usually necessary to include a functional residual E i (t id ) (or functional random intercept per curve) as one of the h j (x i , t id ) in (1).…”

“…While simple random intercepts imply a compound symmetry correlation matrix marginally, marginalization becomes even more challenging for more complex random effects structures. A related point appears in the context of GAMLSS-type (generalized additive models for location, scale and shape) functional response models (Stöcker et al 2018), where conditioning on functional residuals means that only the measurement error variance is allowed to vary according to an additive predictor. Ideally, we would like to model both the residual (marginal) variance as well as the remaining (marginal) functional covariance structure depending on covariates.…”

Boosting Functional Regression Models with FDboost

“…The combination of GAMLSS with functional variables is discussed in Brockhaus et al (2018) and Stöcker et al (2018). For GAMLSS models, FDboost builds on the package gamboost-LSS (Hofner, Mayr, Fenske, Thomas, and Schmid 2020), in which families are implemented to fit GAMLSS.…”