Abstract

We develop a regression model for spatially dependent binary response variables when the covariates take the form of functional processes over time at each location for which the response is observed. We model the functional covariates in terms of a Fourier basis truncated to a finite number of terms. Responses are taken to be a Markov random field with conditional binary distributions and isotropic spatial dependence. Estimation is approached through the use of a composite likelihood constructed from full conditional response distributions, sometimes also called Besag’s original pseudolikelihood in the spatial literature. Asymptotic properties are given for maximum composite likelihood estimators using a repeating lattice context, and use of the model is illustrated with data relating new COVID vaccination rates in June for counties to the number of weekly infections reported over the previous several months in those same counties.