Spatial confounding beyond generalized linear mixed models: extension to shared components and spatial frailty models

Abstract

Spatial confounding is the name given to the confounding between fixed and spatial random effects in generalized linear mixed models (GLMMs). It has been widely studied and it gained attention in the past years in the spatial statistics literature, as it may generate unexpected results in modeling. The projection-based approach, also known as restricted models, appears like a good way to overcome the spatial confounding in this kind of models. However, when the support of fixed effects is different from the spatial effect one or when multiple spatial effects are present in the modeling, this approach can no longer be applied directly. In this work, we introduce solutions to alleviate the spatial confounding for two families of statistical models. In shared component models, multiple count responses are recorded at each spatial location, which may exhibit similar spatial patterns. Therefore, the spatial effect terms may be shared between the outcomes in addition to specific spatial patterns. In this case, our proposal relies on the use of modified spatial structures for each shared component and specific effects. Spatial frailty models can incorporate spatially structured effects and it is common to observe more than one sample unit per area which means that the support of fixed and spatial effects differ. In this case, we introduce a projection-based approach reducing the dimensionality of the data. As a product of this work an R package named "RASCO: An R package to Alleviate Spatial Confounding" is provided and it allows the community to alleviate the spatial confounding in GLMMs, shared component models and spatial frailty models. To provide a fast inference for the parameters, we used the INLA methodology. Lung and bronchus cancer in the California state is investigated under both methodologies and the results prove the efficiency of the proposed models.