Sliced Inverse Regression for Spatial Data

TL;DR

This paper extends sliced inverse regression to spatially dependent data on grid structures, providing guidelines for dimension selection and spatial lag importance, supported by simulation results.

Contribution

It introduces a method for applying sliced inverse regression to spatial data with dependencies, including dimension and lag selection guidelines.

Findings

Guidelines for dimension of subspace

Recommendations on spatial lag selection

Simulation study supports the proposed methods

Abstract

Sliced inverse regression is one of the most popular sufficient dimension reduction methods. Originally, it was designed for independent and identically distributed data and recently extend to the case of serially and spatially dependent data. In this work we extend it to the case of spatially dependent data where the response might depend also on neighbouring covariates when the observations are taken on a grid-like structure as it is often the case in econometric spatial regression applications. We suggest guidelines on how to decide upon the dimension of the subspace of interest and also which spatial lag might be of interest when modeling the response. These guidelines are supported by a conducted simulation study.