A penalized likelihood for multispecies occupancy models improves predictions of species interactions

Multispecies occupancy models estimate dependence among multiple species of interest from patterns of co-occurrence, but problems associated with separation and boundary estimates can lead to unreasonably large estimates of parameters and associated standard errors when species are rarely observed at the same site or when data are sparse. In this paper, we overcome these issues by implementing a penalized likelihood, which introduces a small bias in parameter estimates in exchange for a potentially large reduction in variance. We compare parameter estimates obtained from both penalized and unpenalized multispecies occupancy models fit to simulated data that exhibit various degrees of separation and to a real-word data set of bird surveys with little apparent overlap between potentially interacting species. Our simulation results demonstrate that penalized multispecies occupancy models did not exhibit boundary estimates and produced lower bias, lower mean squared error, and improved inference relative to unpenalized models. When applied to real-world data, our penalized multispecies occupancy model constrained boundary estimates and allowed for meaningful inference related to the interactions of two species of conservation concern. To facilitate the use of our penalized multispecies occupancy model, the techniques demonstrated in this paper have been integrated into the unmarked package in R programing language.