A common sampling design in resource selection studies involves measuring resource attributes at sample units used by an animal and at sample units considered available for use. Few models can estimate the absolute probability of using a sample unit from such data, but such approaches are generally preferred over statistical methods that estimate a relative probability of use. The case-control model that allows for contaminated controls, proposed by Lancaster & Imbens (1996) and Lele (2009), can estimate the absolute probability of using a sample unit from use-availability data. However, numerous misconceptions have likely prevented the widespread application of this model to resource selection studies. We address common misconceptions regarding the case-control model with contaminated controls and demonstrate its ability to estimate the absolute probability of use, prevalence and parameters associated with categorical covariates from use-availability data. We fit the case-control model with contaminated controls to simulated data with varying prevalence (defined as the average probability of use across all sample units) and sample sizes (n1 = 500 used and na = 500 available samples; n1 = 1000 used and na = 1000 available samples). We then applied this model to estimate the probability Ozark hellbenders (Cryptobranchus alleganiensis bishopi) would use a location within a stream as a function of covariates. The case-control model with contaminated controls provided unbiased estimates of all parameters at N = 2000 sample size simulation scenarios, particularly at low prevalence. However, this model produced increasingly variable maximum likelihood estimates of parameters as prevalence increased, particularly at N = 1000 sample size scenarios. We thus recommend at least 500-1000 used samples when fitting the case-control model with contaminated controls to use-availability data. Our application to hellbender data revealed selection for locations with coarse substrate that are close to potential sources of cover. This study unites a disparate literature, addresses and clarifies many commonly held misconceptions and demonstrates that the case-control model with contaminated controls is a viable alternative for estimating the absolute probability of use from use-availability data.
- Bayesian analysis
- Data cloning
- Markov chain Monte Carlo sampling
- Maximum partial likelihood estimator