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.

中文翻译：

---

可修改面积单位问题 (MAUP) 对遗漏误差的影响

当回归模型中缺少自变量时，就会发生遗漏错误。当单个观测值不可用时，可修改面积单位问题 (MAUP) 与空间聚合数据集一起出现。遗漏误差和 MAUP 都可以在回归分析中同时发生。特别是，MAUP 会导致由于遗漏误差而导致的偏差对于线性回归模型更难以预测，并且它会随着不同的空间配置而以不同的方式扭曲偏差。本文分析了 MAUP 对遗漏误差的影响，表明总体水平的系数估计期望可以分解为三个部分：真实系数、个体水平偏差和总体水平偏差。这些发现填补了地理学实证研究与计量经济学理论结果之间的空白，