  Occupancy models are used in statistical ecology to estimate species
dispersion. The two components of an occupancy model are the detection and
occupancy probabilities, with the main interest being in the occupancy
probabilities.
  We show that for the homogeneous occupancy model there is an orthogonal
transformation of the parameters that gives a natural two-stage inference
procedure based on a conditional likelihood. We then extend this to a partial
likelihood that gives explicit estimators of the model parameters. By allowing
the separate modelling of the detection and occupancy probabilities, the
extension of the two-stage approach to more general models has the potential to
simplify the computational routines used there.
