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. 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 develop 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 parameter function. A binary conditionals model is presented as a concrete illustration and is used in simulation studies to verify the applicability of the asymptotic inferential results.

翻译：我们将独立的广义函数型线性模型扩展至函数型协变量与表现出空间依赖性的标量响应变量相关的情形。在估计过程中，我们采用基展开和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。在重复格点渐近框架下，我们推导了所提出模型的渐近性质，从而能够构建空间依赖参数的置信区间和参数函数的置信带。作为具体实例，我们提出了二元条件模型，并通过模拟研究验证了渐近推断结果的适用性。