Spatiotemporal analysis and modeling have long been key foci of geographical information science. In a recent paper, Wu et al. expanded the local spatial modeling technique of multiscale geographically weighted regression (MGWR) to incorporate a temporal component. This new model is named multiscale geographically and temporally weighted regression (MGTWR). Despite the utility of expanding MGWR to incorporate a temporal weighting function in addition to the existing spatial one, the approach developed by Wu et al. has two limitations: the bandwidth selection algorithm cannot guarantee an optimal result and no formulation for the effective number of parameters (ENPs) in the model is given. To address these issues, this paper describes a procedure to derive an optimal temporal and an optimal spatial bandwidth for MGTWR and also develops a formula for the ENPs in the model. The former ensures the reliability of the model outputs while the latter is essential for making reliable inferences from the local parameter estimates generated in the calibration of models by MGTWR. These advances in the MGTWR framework are demonstrated through applications to simulated and real-world data.

A recent addition to the suite of techniques for local statistical modeling is the implementation of the multiscale geographically weighted regression (MGWR), a multiscale extension to geographically weighted regression (GWR). Using a back-fitting algorithm, MGWR relaxes the restrictive assumption in GWR that all processes being modeled operate at the same spatial scale and allows the estimation of a unique indicator of scale, the bandwidth, for each process. However, the current MGWR framework is limited to use with continuous data making it unsuitable for modeling data that do not typically exhibit a Gaussian distribution. This study expands the application of the MGWR framework to scenarios involving discrete response outcomes (count data following a Poisson’s distribution). Use of this new MGWR Poisson regression (MGWPR) model is demonstrated with a simulated data set and then with COVID-19 case counts within New York City at the zip code level. The results from the simulated data underscore the superiority of the MGWPR model in effectively capturing spatial processes that influence count data patterns, particularly those operating across diverse spatial scales. For empirical data, the results reveal significant spatial variations in relationships between socio-ecological factors and COVID-19 cases – variations often missed by traditional ‘global’ models.

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.

The measurement of spatial dependence within a set of observations or the residuals from a regression is one of the most common operations within spatial analysis. However, there appears to be a lack of appreciation for the fact that these measurements are generally based on an a priori definition of a spatial weights matrix and hence are limited to detecting spatial dependence at a single spatial scale. This paper highlights the scale-dependence problem with current measures of spatial dependence and defines a new, multi-scale approach to defining a spatial weights matrix based on a discrete Fourier transform. This approach is shown to be able to detect statistically significant spatial dependence which other multi-scale approaches to measuring spatial dependence cannot. The paper thus serves as a warning not to rely on traditional measures of spatial dependence and offers a more comprehensive, and scale-free, approach to measuring such dependence.

A recent paper in this journal proposed a form of geographically weighted regression (GWR) that is termed parameter-specific distance metric geographically weighted regression (PSDM GWR). The central focus of the PSDM generalization of the GWR framework is that it allows the kernel function that weights nearby data to be specified with a distinct distance metric. As with the recent paper on Multiscale GWR (MGWR), the PSDM framework presents a form of GWR that also allows for parameter-specific bandwidths to be computed. As a result, a secondary focus of the PSDM GWR framework is to reduce the computational overhead associated with searching a massive parameter space to find a set of optimal parameter-specific bandwidths and parameter-specific distance metrics. In this comment, we discuss several concerns with the PSDM GWR framework in terms of model interpretability, complexity, and computational efficiency. We also recommend some best practices when using these models, suggest how to more holistically assess model variations, and set out an agenda to constructively focus future research endeavors.