Smooth Post-Stratification in Multiple Capture-Recapture

• Activity Number: 572
• Type: Invited
• Date/Time: Wednesday, August 7, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Social Statistics Section
• Author(s): Zachary T. Kurtz*+
• Companies: Carnegie Mellon University, Dept. of Stat.
• Keywords: Capture-Recapture ; Conditional Density ; Log-Linear Models ; Post-Stratification

Abstract

Capture-recapture (CRC) is a way to estimate the size of a population by combining incomplete lists of population units. For the two-list scenario, the oldest estimator is the Petersen estimator, which assumes that the event of capture on the first list is independent of the event that a unit is captured on the second list. Because this assumption is usually false, the Petersen estimator is biased for most applications. Literature on overcoming the bias in the Petersen estimates tends to fall into one of two groups. The first group of models expresses capture probabilities as functions of capture pattern in ways that allow for complex interactions between lists in the aggregate -- without explicitly modeling covariate effects. The second group of models regresses capture probabilities conditional on covariates. Post-stratification is a discrete way to condition on covariates. However, continuous generalizations (i.e., smooth post-stratification models) typically assume a strong form of independence between lists which is not optimal in the case of three or more lists. We combine these two lines of work to produce an estimator that models complex list interactions locally.