A Bayesian modified case-control model for estimating absolute probability of use from use-availability data

Background/Question/Methods

A use-availability sampling design is commonly employed in resource selection studies.  Under a use-availability design, a sample of used sites is selected from the subpopulation of used sites and a sample of available sites is selected from the entire population. Commonly used analytical approaches for such data estimate a resource selection index that is assumed proportional to the absolute probability of use, but recent work has demonstrated that such proportionality is not guaranteed.  Additionally, a small number of recently developed models are capable of estimating absolute probability of use from use-availability data, but these models require data on all resource units considered available.  The modified case-control model of Lancaster and Imbens (1996, Journal of Econometrics) may be an alternative to estimating the absolute probability of use from use-availability data but has been described as difficult to implement and unstable.  We first proposed a Bayesian alternative to the modified case-control model.  We then conducted a simulation study using both a maximum-likelihood (MLE) and a Bayesian implementation.  We explored model behavior over varying levels of prevalence (defined as the unconditional probability of occurrence) and sample size.  Finally, we used this model to estimate Ozark hellbender (Cryptobranchus alleganiensis bishopi) resource selection.

Results/Conclusions

Bayesian models achieved nominal coverage of all parameters (95% credible intervals contained the data-generating value of parameters in approximately 95% of simulations) over all levels of prevalence and sample size.  However, Bayesian point estimates of the intercept parameter (defined as the mean of the estimated posterior distribution) were biased high in low prevalence and sample size scenarios.  In contrast, MLE models achieved nominal coverage of all parameters only in intermediate prevalence and large sample size scenarios. In low prevalence scenarios, MLE models underestimated both the intercept parameter and prevalence, regardless of sample size.  The MLE models also underestimated the intercept parameter in high prevalence and low sample size scenarios.  Bayesian and MLE models fit to hellbender data produced almost identical estimates of regression coefficients describing the strength and direction of resource selection.  Additionally, Bayesian models estimated low hellbender prevalence, whereas MLE models were unable to provide meaningful prevalence estimates, highlighting the difficulties of fitting MLE models at low prevalence.  Our simulations and application to hellbender data suggest that barriers to implementation of the modified case-control model can be overcome and that this model offers a viable alternative for estimating resource selection from use-availability designs.