On a Linear Functional Mixed Effect Model for Spatial Data

Abstract

This paper introduces a functional mixed effect random model to model spatial data. In this model, the spatial locations form the index set, while the contributing effects to the response variable are set as a linear mixture of fixed and random effects. These fixed and random effects are linear combinations of L2 functions and random elements, respectively. However, the corresponding linear factors depend on the spatial location variable. Therefore, we develop estimation procedures to estimate the fixed and random coefficients, using spatial functional principal component analysis. Then, we perform prediction by adapting the functional universal kriging method to our model.