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arXiv · 2403.03389

Exploring Spatial Generalized Functional Linear Models: A Comparative Simulation Study and Analysis of COVID-19

Sooran Kim·Mark S. Kaiser·Xiongtao Dai
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Abstract

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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Sooran Kim, Mark S. Kaiser, Xiongtao Dai. 2024-12-23. Exploring Spatial Generalized Functional Linear Models: A Comparative Simulation Study and Analysis of COVID-19. https://arxiv.org/abs/2403.03389

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