Functional Concurrent Linear Regression Model for Spatial Images

Abstract

Motivated by a problem in describing forest nitrogen cycling, in this paper we explore regression models for spatial images. Specifically, we present a functional concurrent linear model with varying coefficients for two-dimensional spatial images. To address overparameterization issues, the parameter surfaces in this model are transformed into the wavelet domain and a sparse representation is found by using a large-scale l1 constrained least squares algorithm. Once the sparse representation is identified, an inverse wavelet transform is applied to obtain the estimated parameter surfaces. The optimal penalization term in the objective function is determined using the Bayesian Information Criterion (BIC) and we introduce measures of model quality. Our model is versatile and can be applied to both single and multiple replicate cases.