  Site occupancy models are routinely used to estimate the probability of
species presence from either abundance or presence-absence data collected
across sites with repeated sampling occasions. In the last two decades, a broad
class of occupancy models has been developed, but little attention has been
given to examining the effects of heterogeneity in parameter estimation. This
study focuses on occupancy models where heterogeneity is present in detection
intensity and the presence probability. We show that the presence probability
will be underestimated if detection heterogeneity is ignored. On the other
hand, the behavior is different if heterogeneity in the presence probability is
ignored; notably, an estimate of the average presence probability may be
unbiased or over- or under-estimated depending on the relationship between
detection and presence probabilities. In addition, when heterogeneity in the
detection intensity is related to covariates, we propose a conditional
likelihood approach to estimate the detection intensity parameters. This
alternative method shares an optimal estimating function property and it
ensures robustness against model specification on the presence probability. We
then propose a consistent estimator for the average presence probability,
provided that the detection intensity component model is correctly specified.
We illustrate the bias effects and estimator performance in simulation studies
and real data analysis.
