On the existence of maximum likelihood estimates for presence-only data

Methods in Ecology and Evolution

By: Trevor J. Hefley and Mevin Hooten

Presence-only data can be used to determine resource selection and estimate a species’ distribution. Maximum likelihood is a common parameter estimation method used for species distribution models. Maximum likelihood estimates, however, do not always exist for a commonly used species distribution model – the Poisson point process.
We demonstrate the issue with conventional maximum likelihood mathematically, using a data example, and a simulation experiment and show alternative estimation methods.
We found that when habitat preferences are strong or the number of presence-only locations is small, by chance, maximum likelihood coefficient estimates for the Poisson point process model may not exist. We found that several alternative estimation methods can produce reliable estimates, but results will depend on the chosen method.
It is important to identify conditions for which maximum likelihood estimates are unlikely to be identifiable from presence-only data. In data sets where the maximum likelihood estimates do not exist, penalized likelihood and Bayesian methods will produce coefficient estimates, but these are sensitive to the choice of estimation procedure and prior or penalty term. When sample size is small or it is thought that habitat preferences are strong, we propose a suite of estimation procedures researchers can consider using.

Additional publication details
Publication type	Article
Publication Subtype	Journal Article
Title	On the existence of maximum likelihood estimates for presence-only data
Series title	Methods in Ecology and Evolution
DOI	10.1111/2041-210X.12340
Volume	6
Issue	6
Year Published	2015
Language	English
Publisher	British Ecological Society
Contributing office(s)	Coop Res Unit Seattle
Description	8 p.
First page	648
Last page	655
Online Only (Y/N)	N
Additional Online Files (Y/N)	N
Google Analytic Metrics	Metrics page