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

TL;DR

This paper compares methods for selecting truncation levels in spatial generalized linear models with functional covariates, demonstrating BIC as a preferred criterion and applying the model to analyze COVID-19 vaccination and case data.

Contribution

It introduces a comparative study of truncation level selection criteria and advocates for BIC, enhancing the application of spatial functional generalized linear models.

Findings

BIC is recommended as a default criterion for truncation level selection.

Spatial models with functional covariates outperform others when spatial structure is present.

Application to COVID-19 data reveals relationships between vaccination rates and case numbers.

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.