Poisson and Logistic Regressions for Inhomogeneous Multivariate Point Processes: A Case Study in the Barro Colorado Island Plot

This study aims to extend the estimating equations based on the Poisson and logistic regression likelihoods to model the intensity of a multivariate point process. The proposed approaches result in a framework equivalent to the estimation procedure for generalized linear model. The estimation is different from the existing methods where repetition independently with respect to the number of types of point process is obliged. Our approach does not require repetition and hence could be computationally faster. We implement our method to analyze the distribution of 9-species of trees in the Barro Colorado Island rainforest with respect to 11-environmental variables.