This study proposes a mathematical programming-based algorithm for the integrated selection of variable subsets and bandwidth estimation in geographically weighted regression, a local regression method that allows the kernel bandwidth and regression coefficients to vary across study areas. Unlike standard approaches in the literature, in which bandwidth and regression parameters are estimated separately for each focal point on the basis of different criteria, our model uses a single objective function for the integrated estimation of regression and bandwidth parameters across all focal points, based on the regression likelihood function and variance modeling. The proposed model further integrates a procedure to select a single subset of independent variables for all focal points, whereas existing approaches may return heterogeneous subsets across focal points. We then propose an alternative direction method to solve the nonconvex mathematical model and show that it converges to a partial minimum. The computational experiment indicates that the proposed algorithm provides competitive explanatory power with stable spatially varying patterns, with the ability to select the best subset and account for additional constraints.

Inspired by the success of Geographically Weighted Regression and its accounting for spatial variations, we propose GeogGNN -- A graph neural network model that accounts for geographical latitude and longitudinal points. Using a synthetically generated dataset, we apply the algorithm for a 4-class classification problem in cybersecurity with seemingly realistic geographic coordinates centered in the Gulf Cooperation Council region. We demonstrate that it has higher accuracy than standard neural networks and convolutional neural networks that treat the coordinates as features. Encouraged by the speed-up in model accuracy by the GeogGNN model, we provide a general mathematical result that demonstrates that a geometrically weighted neural network will, in principle, always display higher accuracy in the classification of spatially dependent data by making use of spatial continuity and local averaging features.

Demographic and educational factors are essential, influential factors of early childhood development. This study aimed to investigate spatial patterns in the association between attendance at preschool and children's developmental vulnerabilities in one or more domain(s) in their first year of full-time school at a small area level in Queensland, Australia. This was achieved by applying geographically weighted regression (GWR) followed by K-means clustering of the regression coefficients. Three distinct geographical clusters were found in Queensland using the GWR coefficients. The first cluster covered more than half of the state of Queensland, including the Greater Brisbane region, and displays a strong negative association between developmental vulnerabilities and attendance at preschool. That is, areas with high proportions of preschool attendance tended to have lower proportions of children with at least one developmental vulnerability in the first year of full-time school. Clusters two and three were characterized by stronger negative associations between developmental vulnerabilities, English as the mother language, and geographic remoteness, respectively. This research provides evidence of the need for collaboration between health and education sectors in specific regions of Queensland to update current service provision policies and to ensure holistic and appropriate care is available to support children with developmental vulnerabilities.

The geographically weighted regression (GWR) is an essential tool for estimating the spatial variation of relationships between dependent and independent variables in geographical contexts. However, GWR suffers from the problem that classical linear regressions, which compose the GWR model, are more prone to be underfitting, especially for significant volume and complex nonlinear data, causing inferior comparative performance. Nevertheless, some advanced models, such as the decision tree and the support vector machine, can learn features from complex data more effectively while they cannot provide explainable quantification for the spatial variation of localized relationships. To address the above issues, we propose a geographically gradient boosting weighted regression model, GWRBoost, that applies the localized additive model and gradient boosting optimization method to alleviate underfitting problems and retains explainable quantification capability for spatially-varying relationships between geographically located variables. Furthermore, we formulate the computation method of the Akaike information score for the proposed model to conduct the comparative analysis with the classic GWR algorithm. Simulation experiments and the empirical case study are applied to prove the efficient performance and practical value of GWRBoost. The results show that our proposed model can reduce the RMSE by 18.3% in parameter estimation accuracy and AICc by 67.3% in the goodness of fit.

Using geospatial methods, this paper informs the evolving field of research on the diffusion of residential Third Party Owned PV systems by analyzing 1) the spatial distribution of TPO systems, and 2) the influence of demographics on the adoption on the local level. This research is part of a multidisciplinary study into the diffusion of solar technology (SEEDS), using San Diego County as focus area. Our findings reveal a significant clustering of TPO PV adoption in San Diego County. TPO systems reached a similarly high market share across a large area in the central county in contrast to the installation of host-owned systems, which have been less evenly distributed across single-family households in the same area. The diffusion of TPO systems in San Diego County can be partially explained by looking at median income and percentage of people born in the US. The explanatory power of the model varies across the region.