On the measurement of bias in geographically weighted regression models

Hanchen Yu, A. Stewart Fotheringham, Ziqi Li, Taylor Oshan, Levi John Wolf

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


Under the realization that Geographically Weighted Regression (GWR) is a data-borrowing technique, this paper derives expressions for the amount of bias introduced to local parameter estimates by borrowing data from locations where the processes might be different from those at the regression location. This is done for both GWR and Multiscale GWR (MGWR). We demonstrate the accuracy of our expressions for bias through a comparison with empirically derived estimates based on a simulated dataset with known local parameter values. By being able to compute the bias in both models we are able to demonstrate the superiority of MGWR. We then demonstrate the utility of a corrected Akaike Information Criterion statistic in finding optimal bandwidths in both GWR and MGWR as a trade-off between minimizing both bias and uncertainty. We further show how bias in one set of local parameter estimates can affect the bias in another set of local estimates. The bias derived from borrowing data from other locations appears to be very small.

Original languageEnglish (US)
Article number100453
JournalSpatial Statistics
StatePublished - Aug 2020


  • Bias
  • Geographically weighted regression
  • Multiscale geographically weighted regression

ASJC Scopus subject areas

  • Statistics and Probability
  • Computers in Earth Sciences
  • Management, Monitoring, Policy and Law


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