Geographically weighted correspondence matrices for local error reporting and change analyses: mapping the spatial distribution of errors and change

This letter describes and applies generic methods for generating local measures from the correspondence table. These were developed by integrating the functionality of two existing R packages: gwxtab and diffeR. They demonstrate how spatially explicit accuracy and error measures can be generated from local geographically weighted correspondence matrices, for example to compare classified and reference data (predicted and observed) for error analyses, and classes at times t1 and t2 for change analyses. The approaches in this letter extend earlier work that considered the measures derived from correspondence matrices in the context of generalized linear models and probability. Here the methods compute local, geographically weighted correspondence matrices, from which local statistics are directly calculated. In this case a selection of the overall and categorical difference measures proposed by Pontius and Milones (2011) and Pontius and Santacruz (2014), as well as spatially distributed estimates of kappa coefficients, User and Producer accuracies. The discussion reflects on the use of the correspondence matrix in remote sensing research, the philosophical underpinnings of local rather than global approaches for modelling landscape processes and the potential for policy and scientific benefits that local approaches support

Geographically weighted elastic net logistic regression

This paper develops a localized approach to elastic net logistic regression, extending previous research describing a localized elastic net as an extension to a localized ridge regression or a localized lasso. All such models have the objective to capture data relationships that vary across space. Geographically weighted elastic net logistic regression is first evaluated through a simulation experiment and shown to provide a robust approach for local model selection and alleviating local collinearity, before application to two case studies: county-level voting patterns in the 2016 USA presidential election, examining the spatial structure of socio-economic factors associated with voting for Trump, and a species presence–absence data set linked to explanatory environmental and climatic factors at gridded locations covering mainland USA. The approach is compared with other logistic regressions. It improves prediction for the election case study only which exhibits much greater spatial heterogeneity in the binary response than the species case study. Model comparisons show that standard geographically weighted logistic regression over-estimated relationship non-stationarity because it fails to adequately deal with collinearity and model selection. Results are discussed in the context of predictor variable collinearity and selection and the heterogeneities that were observed. Ongoing work is investigating locally derived elastic net parameters