探索空间广义函数线性模型：一项比较模拟研究与 COVID-19 分析
Exploring Spatial Generalized Functional Linear Models: A Comparative Simulation Study and Analysis of COVID-19
AI总结：
本文比较了空间广义函数线性模型中截断水平选择的五种准则，提出 BIC 为合理的默认标准，并证明该模型在含空间结构数据中优于其他模型，成功应用于分析美国中西部 COVID-19 疫苗接种率与新发病例数的关系。
摘要：
带有函数协变量的空间广义线性模型的实现，可以通过对协变量过程使用截断基展开来完成。在实际应用中，必须选择一个截断水平以供使用。我们比较了用于选择适当截断水平的五个准则，包括基于对数复合似然的 AIC 和 BIC、方差解释比例准则、拟合均方误差，以及带有一个标准误差规则的预测误差。基于广泛的模拟研究，我们提出 BIC 构成了在空间函数广义线性模型中选择截断水平的一个合理的默认准则。此外，我们证明了当数据包含空间结构且响应变量实际上受函数协变量过程影响时，带有函数协变量的空间模型优于其他模型。我们将空间函数广义线性模型应用于一个问题，其目标是将美国中西部各州各县的 COVID-19 疫苗接种率与相同地理区域前几周的新发病例数联系起来。
英文摘要：
Implementation of spatial generalized linear models with a functional covariate can be accomplished through the use of a truncated basis expansion of the covariate process. In practice, one must select a truncation level for use. We compare five criteria for the selection of an appropriate truncation level, including AIC and BIC based on a log composite likelihood, a fraction of variance explained criterion, a fitted mean squared error, and a prediction error with one standard error rule. Based on the use of extensive simulation studies, we propose that BIC constitutes a reasonable default criterion for the selection of the truncation level for use in a spatial functional generalized linear model. In addition, we demonstrate that the spatial model with a functional covariate outperforms other models when the data contain spatial structure and response variables are in fact influenced by a functional covariate process. We apply the spatial functional generalized linear model to a problem in which the objective is to relate COVID-19 vaccination rates in counties of states in the Midwestern United States to the number of new cases from previous weeks in those same geographic regions.
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