Boosting Functional Response Models for Location, Scale and Shape with an Application to Bacterial Competition
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We extend Generalized Additive Models for Location, Scale, and Shape (GAMLSS) to regression with functional response. GAMLSS are a flexible model class allowing for modeling multiple distributional parameters at once. By expanding these models to functional regression, we may, e.g., model both mean and variance curves for the response over time and depending on covariates. For each distributional parameter, a separate functional additive model equation can be specified, including various scalar and functional covariate effects. In addition, a variety of exponential family and non-exponential family probability distributions can be specified for the response measurements. The model is fitted via gradient boosting, which provides inherent model selection and suitable regularization to face both complex model structures and high in-curve dependencies in reponse curves. The new model class enables us to analyze bacterial interaction in Escherichia coli in a complex data setting and, thereby, show how the modeling of variance structure and extinction probabilities fruitfully extends usual growth models.
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