Generalized functional additive mixed models with (functional) compositional covariates for areal Covid-19 incidence curves

Abstract

We extend the generalized functional additive mixed model to include compositional and functional compositional (density) covariates carrying relative information of a whole. Relying on the isometric isomorphism of the Bayes Hilbert space of probability densities with a sub-space of the L2, we include functional compositions as transformed functional covariates with constrained yet interpretable effect function. The extended model allows for the estimation of linear, non-linear, and time-varying effects of scalar and functional covariates, as well as (correlated) functional random effects, in addition to the compositional effects. We use the model to estimate the effect of the age, sex, and smoking (functional) composition of the population on regional Covid-19 incidence data for Spain, while accounting for climatological and socio-demographic covariate effects and spatial correlation.