Validating Geospatial Regression Models With Bootstrapping

TL;DR: The study showed that bootstrapping can reveal the differences between empirical (bootstrap) distributions and those based on theoretical asymptotic assumptions in a forthright and sound fashion, allowing a spatial regression model to be validated effectively.

Abstract: Spatial statistical models have been used extensively in many geospatial and environmental studies over several decades. While being very important, the issues of testing and validation in spatial statistical models are rarely investigated carefully in spatial environmental studies. Often strict theoretical asymptotic assumptions used in those models are left unexplored or unanswered in many studies. This study is to explore if bootstrapping is capable of providing more realistic statistical inference for spatial regression models while dealing with several common issues with spatial data, such as spatial dependence and unknown heteroscedasticity. With experiments on both simulated and real-world datasets, the study showed that bootstrapping can reveal the differences between empirical (bootstrap) distributions and those based on theoretical asymptotic assumptions in a forthright and sound fashion, allowing a spatial regression model to be validated effectively. Such validation arguably is very important to geospatial and environmental studies, especially those with small sample sizes. Hence, bootstrapping should be used widely as a second line of evidence for statistical inference in spatial environmental studies.