The Impacts of the Modifiable Areal Unit Problem (MAUP) on Omission Error

An omission error occurs when independent variables are missing from a regression model. When individual observations are not available, the modifiable areal unit problem (MAUP) appears with spatially aggregated data sets. Both omission error and the MAUP can occur simultaneously in regression analyses. In particular, the MAUP causes the bias due to an omission error to be less predictable for linear regression models, and it distorts bias differently with different spatial configurations. This article analyses the impacts of the MAUP on omission error and shows that the expectation of coefficient estimates at the aggregate level can be decomposed into three parts: the true coefficient, individual-level bias, and aggregate-level bias. The findings fill the gap between empirical studies in geography and theoretical results in econometrics, and show that the traditional approaches to the MAUP, such as reporting analyses from multiple spatial configurations, are unhelpful in identifying the correct coefficients.