Local Log-linear Models for Capture-Recapture

Log-linear models are often used to estimate the size of a closed population using capture-recapture data. When capture probabilities are related to auxiliary covariates, one may select a separate model based on each of several post-strata. We extend post-stratification to its logical extreme by selecting a local log-linear model for each observed unit, while smoothing to achieve stability. Our local models serve a dual purpose: In addition to estimating the size of the population, we estimate the rate of missingness as a function of covariates. A simulation demonstrates the superiority of our method when the generating model varies over the covariate space. Data from the Breeding Bird Survey is used to illustrate the method.