A Comparison of Spatially Varying Regression Coefficient Estimates Using Geographically Weighted and Spatial‐Filter‐Based Techniques

Geographically weighted regression (GWR) is a technique that explores spatial nonstationarity in data‐generating processes by allowing regression coefficients to vary spatially. It is a widely applied technique across domains because it is intuitive and conforms to the well‐understood framework of regression. An alternative method to GWR that has been suggested is spatial filtering, which it has been argued provides a superior alternative to GWR by producing spatially varying regression coefficients that are not correlated with each other and which display less spatial autocorrelation. It is, therefore, worthwhile to examine these claims by comparing the output from both methods. We do this by using simulated data that represent two sets of spatially varying processes and examining how well both techniques replicate the known local parameter values. The article finds no support that spatial filtering produces local parameter estimates with superior properties. The results indicate that the original spatial filtering specification is prone to overfitting and is generally inferior to GWR, while an alternative specification that minimizes the mean square error (MSE) of coefficient estimates produces results that are similar to GWR. However, since we generally do not know the true coefficients, the MSE minimizing specification is impractical for applied research.     

War widows and revenge in Restoration England

This article examines petitions submitted by royalist widows to the House of Lords during the first few months of the Restoration. The husbands of these women had been tried and executed for treason during the 1640s and 1650s for their perceived loyalty to the royalist cause, prompting their spouses to demand retribution against their judges and jurors. As the Convention Parliament deliberated over the Act of Indemnity during the summer of 1660, these aggrieved widows were presented with an opportunity to ensure that the men they held responsible for their husband’s deaths were brought to account. By assessing the petitioning strategies adopted by these women and the government’s responses to their demands, the article throws light on a group of war widows who have received little scholarly attention. It is argued that whilst these women were largely unsuccessful, their efforts represent a significant aspect of female activism during the seventeenth century.