Although geographically weighted Poisson regression (GWPR) is a popular regression for spatially indexed count data, its development is relatively limited compared to that found for linear geographically weighted regression (GWR), where many extensions (e.g., multiscale GWR, scalable GWR) have been proposed. The weak development of GWPR can be attributed to the computational cost and identification problem in the underpinning Poisson regression model. This study proposes linearized GWPR (L-GWPR) by introducing a log-linear approximation into the GWPR model to overcome these bottlenecks. Because the L-GWPR model is identical to the Gaussian GWR model, it is free from the identification problem, easily implemented, computationally efficient, and offers similar potential for extension. Specifically, L-GWPR does not require a double-loop algorithm, which makes GWPR slow for large samples. Furthermore, we extended L-GWPR by introducing ridge regularization to enhance its stability (regularized L-GWPR). The results of the Monte Carlo experiments confirmed that regularized L-GWPR estimates local coefficients accurately and computationally efficiently. Finally, we compared GWPR and regularized L-GWPR through a crime analysis in Tokyo.

翻译：尽管地理加权泊松回归（GWPR）是空间索引计数数据的一种常用回归方法，但与线性地理加权回归（GWR）相比，其发展相对有限——后者已提出多种扩展方法（如多尺度GWR、可扩展GWR）。GWPR发展滞后的原因可归因于其底层泊松回归模型的计算成本与识别问题。本研究通过在线性化GWPR模型中引入对数线性近似，提出了线性化地理加权泊松回归（L-GWPR），以突破上述瓶颈。由于L-GWPR模型与高斯GWR模型等价，因此它不存在识别问题，易于实现、计算高效，并具备类似的扩展潜力。具体而言，L-GWPR无需使用导致大样本GWPR运算缓慢的双循环算法。此外，我们通过引入岭正则化对L-GWPR进行扩展（正则化L-GWPR），以增强其稳定性。蒙特卡洛实验结果表明，正则化L-GWPR能够准确且高效地估计局部系数。最后，我们通过东京的犯罪分析案例，对GWPR与正则化L-GWPR进行了比较。