Recovering the biased estimation of σ^2 in linear regression for spatially aggregated dataset

Keywords: modifiable areal unit problem, liner regression, disturbance, aggregation, uncertainty
Session Type: Virtual Paper Abstract
Day: Saturday
Session Start / End Time: 2/26/2022 08:00 AM (Eastern Time (US & Canada)) - 2/26/2022 09:20 AM (Eastern Time (US & Canada))
Room: Virtual 3

Abstract

In a classical linear regression model (CLRM), the magnitude of disturbance is characterized by σ^2. By adopting the ordinary least square (OLS) method, σ^2 is estimated by s^2, which is an unbiased estimator for σ^2 when individual observations are available. However, if the modifiable areal unit problem (MAUP) appears, individual observations are aggregated into regions, which brings a significant challenge to estimating σ^2, as the traditional estimator becomes systematically downward biased at the aggregate level. To remedy the situation, three alternative estimators of σ^2 are proposed by adopting different amounts of information regarding the aggregation process: the trace estimator, the harmonic estimator, and the arithmetic estimator. Verified by the Monte-Carlo simulation based on synthetic datasets, these three estimators perform substantially better than directly borrowing s^2 at the aggregated level, but each achieves differently for the balance between the accuracy of estimates and the availability of information needed. The findings lay down the theoretical foundation for exploring the role of the MAUP in inferential statistics applied in a regression model, like confidence intervals and hypothesis testing.