This article presents a spatial–temporal generalized additive model for modeling geo-referenced COVID-19 mortality data in Toronto, Canada. A range of factors and spatial–temporal terms are incorporated into the model. The non-linear and interactive effects of the neighborhood-level factors, i.e., population density and average of income, are modeled as a two-dimensional spline smoother. The change of spatial pattern over time is modeled as a three-dimensional tensor product smoother. By fitting this model, the space–time effect can uncover the underlying spatial–temporal pattern that is not explained by the covariates. The performance of the modeling method based on the individual data is also compared to the modeling methods based on the aggregated data in terms of in-sample and out-of-sample predictive checking. The results suggest that the individual-level based analysis provided a better overall model fit and higher predictive accuracy for detecting epidemic peaks in this application as compared to the analysis based on the aggregated data.

本文介绍了一种时空广义相加模型，用于对加拿大多伦多的地理参考 COVID-19 死亡率数据进行建模。模型中包含了一系列因素和时空项。邻域级因素的非线性和交互影响，即人口密度和平均收入，被建模为二维样条平滑器。空间模式随时间的变化被建模为一个三维张量积平滑器。通过拟合该模型，时空效应可以揭示协变量无法解释的潜在时空模式。在样本内和样本外预测检查方面，还将基于个体数据的建模方法与基于聚合数据的建模方法的性能进行了比较。