The multiple recapture census for closed populations and incomplete 2k contingency tables

Abstract

The multiple recapture census for closed populations is reconsidered, assuming an underlying multinomial sampling model. The resulting data can be put in the form of an incomplete 2^k contingency table, with one missing cell, that displays the full multiple recapture history of all individuals in the population. Log linear models are fitted to this incomplete contingency table, and the simplest plausible model that fits the observed cells is projected to cover the miming cell, thus yielding an estimate of the total population size. Asymptotic variances for the estimate of the population size are considered, and the techniques are illustrated on a population of children possessing a common congenital anomaly.