A Rejoinder to the Commentaries on “A Route Map for Successful Applications of Geographically Weighted Regression” by Comber et al. (2022)

Abstract

We are delighted that the RM paper has stimulated three coherent but diverse Commentaries from leading thinkers in this field (Fotheringham, 2022; Oshan, 2022; Wolf, 2022). Each of these contains robust critiques of the proposed RM and suggest alternative but diverse sets of considerations. We consider each of these in turn and provide a rejoinder by way of response.

We thank the authors of these commentaries for their efforts, and for taking the time to consider our article in detail. In general, we are pleased to see these—part of our motivation here was to initiate discussion on approaches to modeling spatial non-stationarity in regression models. By setting out one way to proceed through our RM, we intended to make an opening move. One thing we observe from these responses is that there is perhaps a spectrum for motivation for using these kind of models—at one end, an approach that is strongly motivated by underlying theories, and at the other, a more exploratory approach. One also has to consider the idea of data analysis as compromise—the reality of modern data collection is frequently that of “big data” where datasets are large, but quality and suitability assurance are not to the standards achieved by carefully designed surveys or experiments. In many cases, geographical fluctuations in models may be a consequence of this, and spatially varying coefficient methods may act as “spatial detectives” by shedding light on spatial inconsistencies and biases in the data collection, rather than direct measurements of a true underlying process. This suggests the need for a kind of “deep inference” where processes under investigation and the process of data collection are considered in equal measure, requiring consideration of underlying process theories, in addition to issues relating to the act of data exploration—perhaps suggesting that the spectrum referred to earlier is something to be scanned, rather than choosing a specific viewpoint from which to carry out analysis.

As we stated earlier, the approach outlined in the GWR RM by Comber et al. (2022a) is not intended to be a strict set of immutable rules, but more of an exemplar of what could be done to respond to a specific research context, and acknowledging that a degree of ‘fuzziness’ in modeling strategies is inevitable. The replies to our article have been useful in considering potential alternative research contexts, and how they may interact with this kind of fuzziness. We look forward to the debate advancing.