Estimating occupancy and the two-stage approach

We developed innovative modern statistical
approaches to estimating occupancy, used in ecology, from presence-absence data that update and extend current methods. These approaches accommodate
imperfect detection that may depend on external factors using mixture models.
 
We will resolve some limitations with the full likelihood approach and demonstrate the two-stage approach to occupancy using partial likelihoods. This approach reduces the dimension of model checking and overcomes limitations with the full likelihood. It has computational advantages that allow full access to R functions. We will discuss the homogeneous, heterogeneous and time-dependent likelihood functions. We adapted estimation techniques for the two-stage approach and compared these to standard numerical optimization. Finally, the two-stage approach to occupancy for GLMs is extended to GAMs. 

Methods are demonstrated with real data from ecology and simulations.