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.Comment: bootstrap confidence interval type uncertainty bounds added; minor
changes in formulation
