Generalised functional additive mixed models with compositional covariates for areal Covid-19 incidence curves

TL;DR

This paper develops an advanced statistical model that incorporates compositional covariates to analyze regional Covid-19 incidence, accounting for various demographic, climatological, and spatial factors.

Contribution

It introduces a generalized functional additive mixed model with compositional covariates using Bayes Hilbert space transformations, enabling complex effect estimations.

Findings

Identified the impact of age, sex, and smoking composition on Covid-19 incidence.

Accounted for spatial correlation and other covariates in the model.

Provided a flexible framework for analyzing compositional effects in epidemiological data.

Abstract

We extend the generalised functional additive mixed model to include (functional) compositional covariates carrying relative information of a whole. Relying on the isometric isomorphism of the Bayes Hilbert space of probability densities with a subspace of the $L^2$, we include functional compositions as transformed functional covariates with constrained effect function. The extended model allows for the estimation of linear, nonlinear 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.