We extend generalized functional linear models under independence to a situation in which a functional covariate is related to a scalar response variable that exhibits spatial dependence-a complex yet prevalent phenomenon. For estimation, we apply basis expansion and truncation for dimension reduction of the covariate process followed by a composite likelihood estimating equation to handle the spatial dependency. We establish asymptotic results for the proposed model under a repeating lattice asymptotic context, allowing us to construct a confidence interval for the spatial dependence parameter and a confidence band for the regression parameter function. A binary conditionals model with functional covariates is presented as a concrete illustration and is used in simulation studies to verify the applicability of the asymptotic inferential results. We apply the proposed model to a problem in which the objective is to relate annual corn yield in counties of states in the Midwestern United States to daily maximum temperatures from April to September in those same geographic regions. The extension to an expanding lattice context is further discussed in the supplement.

翻译：本文将独立情形下的广义函数型线性模型扩展至函数型协变量与呈现空间依赖性的标量响应变量相关联的情形——这是一种复杂但普遍存在的现象。在估计方面，我们采用基展开与截断方法对协变量过程进行降维，随后通过复合似然估计方程处理空间依赖性。我们在重复格点渐近框架下建立了所提模型的渐近性质，从而能够构建空间依赖参数的置信区间以及回归参数函数的置信带。本文以具有函数型协变量的二元条件模型作为具体示例，并通过模拟研究验证了渐近推断结果的适用性。我们将所提模型应用于一个实际问题：建立美国中西部各州县域的玉米年产量与同区域四月至九月日最高气温之间的关联。补充材料中进一步讨论了向扩展格点情形的推广。