  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.
