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A new technique called generalized additive spatial smoothing (GASS) is introduced for modeling neighborhood effects within a regression framework. GASS has a number of desirable features, namely that it provides a data-driven mechanism for endogenously selecting neighborhoods based on a spatial scale hyperparameter. By allowing different scale hyperparameters to be selected for different relationships in the model, the technique is inherently multiscale and allows neighborhoods to vary by relationship. In addition, GASS includes a measure of uncertainty associated with each scale hyperparameter. These characteristics make it attractive for modeling phenomena where proximity might be an important aspect of a process, especially when a clear definition of proximity is not immediately available. Through multiscale data-driven spatial smoothing, GASS conducts a form of change of support and therefore also facilitates the incorporation of data from diverse sources. Finally, the technique is flexible and can be adapted and expanded with relative ease because it builds on generalized additive modeling. After providing an overview of the methodology, including a modified backfitting algorithm for calibration, a simulation experiment is described and an empirical example modeling bike-share usage is presented. The simulation results indicate that GASS can generally produce reliable results pertaining to both the regression coefficients and scale hyperparameters, and the results from the empirical example demonstrate that the GASS approach provides a better model fit and captures relationships that might otherwise be obfuscated. Overall, these results highlight the potential of the GASS framework and the importance of measuring multiscale neighborhood effects. [ABSTRACT FROM AUTHOR]

Models designed to capture spatially varying processes are now employed extensively in the social and environmental sciences. The main strength of such models is their ability to represent relationships that vary across locations through locally varying parameter estimates. However, local models of spatial processes also provide information on the nature of these spatially varying relationships through the estimation of a 'bandwidth' parameter. This paper examines bandwidth at a conceptual, operational and empirical level within the framework of geographically weighted regression, one of the more frequently employed local spatial models. We outline how bandwidth relates to three characteristics of spatial processes: variation, dependence and strength. [ABSTRACT FROM AUTHOR]

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Recent work in local spatial modeling has affirmed and broadened interest in multivariate local spatial analysis. Two broad approaches have emerged: Geographically Weighted Regression (GWR) which follows a frequentist perspective and Bayesian Spatially Varying Coefficients models. Although several comparisons between the two approaches exist, recent developments, particularly in GWR, mean that these are incomplete and missing some important axes of comparison. Consequently, there is a need for a more thorough comparison of the two families of local estimators, including recent developments in multiscale variants and their relative performance under controlled conditions. We find that while both types of local models generally perform similarly on a series of criteria, some interesting and important differences exist. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Geographically weighted regression (GWR) is a spatial statistical technique that recognizes that traditional 'global' regression models may be limited when spatial processes vary with spatial context. GWR captures process spatial heterogeneity by allowing effects to vary over space. To do this, GWR calibrates an ensemble of local linear models at any number of locations using 'borrowed' nearby data. This provides a surface of location-specific parameter estimates for each relationship in the model that is allowed to vary spatially, as well as a single bandwidth parameter that provides intuition about the geographic scale of the processes. A recent extension to this framework allows each relationship to vary according to a distinct spatial scale parameter, and is therefore known as multiscale (M)GWR. This paper introduces mgwr, a Python-based implementation of MGWR that explicitly focuses on the multiscale analysis of spatial heterogeneity. It provides novel functionality for inference and exploratory analysis of local spatial processes, new diagnostics unique to multi-scale local models, and drastic improvements to efficiency in estimation routines. We provide two case studies using mgwr, in addition to reviewing core concepts of local models. We present this in a literate programming style, providing an overview of the primary software functionality and demonstrations of suggested usage alongside the discussion of primary concepts and demonstration of the improvements made in mgwr. [ABSTRACT FROM AUTHOR]