  The classical functional linear regression model (FLM) and its extensions,
which are based on the assumption that all individuals are mutually
independent, have been well studied and are used by many researchers. This
independence assumption is sometimes violated in practice, especially when data
with a network structure are collected in scientific disciplines including
marketing, sociology and spatial economics. However, relatively few studies
have examined the applications of FLM to data with network structures. We
propose a novel spatial functional linear model (SFLM), that incorporates a
spatial autoregressive parameter and a spatial weight matrix into FLM to
accommodate spatial dependencies among individuals. The proposed model is
relatively flexible as it takes advantage of FLM in handling high-dimensional
covariates and spatial autoregressive (SAR) model in capturing network
dependencies. We develop an estimation method based on functional principal
component analysis (FPCA) and maximum likelihood estimation. Simulation studies
show that our method performs as well as the FPCA-based method used with FLM
when no network structure is present, and outperforms the latter when network
structure is present. A real weather data is also employed to demonstrate the
utility of the SFLM.
