Omission error in geographically weighted regression

Omission error, or omitted variable bias, arises in regression analysis when an independent variable is excluded from the model, potentially resulting in biased and inconsistent coefficient estimates. In this study, omission error is investigated for geographically weighted regression (GWR), a local regression technique that provides spatially varying coefficients to assess spatial heterogeneities in data relationships. Bias in coefficient estimation caused by omission errors in GWR models is systematically examined, and in doing so, provides a theoretical framework for understanding these impacts through the derivation of a bias term. Via a simulation experiment, omission error characteristics were investigated for both standard and multiscale GWR forms, revealing that omitted variables can strongly influence standard GWR, although kernel bandwidth adjustments can partially mitigate biases. However, multiscale GWR offered much-improved coefficient estimation with reduced bias in respect of omission error. Study findings emphasized the importance of carefully addressing trade-offs between locally correlated independent variables to enhance model estimation robustness and mitigate multicollinearity risks by unintentional omission or deliberate exclusion of variables when following a GWR analysis. Insights into the effects of omission error on composite errors and coefficient variance estimation are also provided.