Measurement error in spatially varying coefficient models

Abstract

Measurement error in explanatory variables can substantially distort regression analysis, affecting both estimation and prediction. While measurement error has been extensively studied in classical regression models, relatively little work has addressed its impact in spatially varying coefficient models.

In this paper, we investigate regression modeling with measurement error in spatial settings and develop estimation procedures for spatially varying coefficient models when covariates are contaminated by measurement error. Our approach integrates the simulation–extrapolation (SIMEX) method with spline-based spatial regression techniques, including bivariate spline triangulation and its penalized version, to correct for measurement error while accommodating spatial heterogeneity.

Through simulation studies on irregular spatial domains and a real data application, we evaluate the performance of the proposed methods in terms of coefficient estimation and prediction accuracy. The results illustrate the practical impact of measurement error on spatial regression and demonstrate the effectiveness of the proposed framework.