We propose a computationally efficient logistic regression estimating function for spatial Gibbs point processes. The sample points for the logistic regression consist of the observed point pattern together with a random pattern of dummy points. The estimating function is closely related to the pseudolikelihood score. However, unlike common implementations of maximum pseudolikelihood, our approach does not suffer from bias due to numerical quadrature. The developed method is implemented in R code and will be added to future versions of the package spatstat. We demonstrate its efficiency and practicability on a real dataset and in a simulation study. Finally, focusing on stationary models, we prove that the estimator derived from the estimating function is strongly consistent and satisfies a central limit theorem. Moreover, we provide a consistent estimate of the asymptotic covariance matrix which allows to construct asymptotic confidence intervals.
Keywords: confidence intervals, estimating functions, exponential family models, Georgii-Nguyen-Zessin formula, logistic regression, pseudolikelihood.
