Abstract
Compositional regression models with a real-valued response variable can generally be specified as log-contrast models subject to a zero-sum constraint on the model coefficients. This formulation emphasises the relative information conveyed in the composition, while the overall total is regarded as irrelevant.
In this work, such a framework is extended to account not only for total effects—formally defined in a so-called T-space—but also for moderation or interaction effects. The approach is implemented in the context of complex spatiotemporal data modelling through an adaptation of the integrated nested Laplace approximation (INLA) method within a Bayesian estimation framework.
Particular emphasis is placed on the interpretation of the model coefficients and results, both on the original scale of the response variable and in terms of elasticities.
The methodology is demonstrated through a detailed case study investigating the relationship between all-cause mortality and the interaction between extreme temperatures, air pollution composition, and total air pollution in Catalonia, Spain, during the summer of 2022.
The results indicate that extreme temperatures are associated with an increased risk of mortality four days after exposure. Additionally, exposure to total air pollution—especially NO₂—is linked to elevated mortality risk regardless of temperature. In contrast, particulate matter is associated with increased mortality only when exposure occurs on days of extreme heat.