Statistical Models for Presence-Only Data: Finite-Sample Equivalence and Addressing Observer Bias

Statistical modeling of presence-only data has attracted much recent attention in the ecological literature, leading to a proliferation of methods, including the inhomogeneous poisson process (IPP) model [15], maximum entropy (Maxent) modeling of species distributions [12] [9] [10], and logistic regression models. Several recent articles have shown the close relationships between these methods [1] [15]. We explain why the IPP intensity function is a more natural object of inference in presence-only studies than occurrence probability (which is only defined with reference to quadrat size), and why presence-only data only allows estimation of relative, and not absolute intensities. All three of the above techniques amount to parametric density estimation under the same exponential family model. We show that the IPP and Maxent models give the exact same estimate for this density, but logistic regression in general produces a different estimate in finite samples. When the model is misspecified, logistic regression and the IPP may have substantially different asymptotic limits with large data sets. We propose “infinitely weighted logistic regression,” which is exactly equivalent to the IPP in finite samples. Consequently, many already-implemented methods extending logistic regression can also extend the Maxent and IPP models in directly analogous ways using this technique. Finally, we address the issue of observer bias, modeling the presenceonly data set as a thinned IPP. We discuss when the observer bias problem can solved by regression adjustment, and additionally propose a novel method for combining presence-only and presence-absence records from one or more species to account for it.