  In this paper we consider the estimation of population size from one-source
capture--recapture data, that is, a list in which individuals can potentially
be found repeatedly and where the question is how many individuals are missed
by the list. As a typical example, we provide data from a drug user study in
Bangkok from 2001 where the list consists of drug users who repeatedly contact
treatment institutions. Drug users with 1, 2, 3$,...$ contacts occur, but drug
users with zero contacts are not present, requiring the size of this group to
be estimated. Statistically, these data can be considered as stemming from a
zero-truncated count distribution. We revisit an estimator for the population
size suggested by Zelterman that is known to be robust under potential
unobserved heterogeneity. We demonstrate that the Zelterman estimator can be
viewed as a maximum likelihood estimator for a locally truncated Poisson
likelihood which is equivalent to a binomial likelihood. This result allows the
extension of the Zelterman estimator by means of logistic regression to include
observed heterogeneity in the form of covariates. We also review an estimator
proposed by Chao and explain why we are not able to obtain similar results for
this estimator. The Zelterman estimator is applied in two case studies, the
first a drug user study from Bangkok, the second an illegal immigrant study in
the Netherlands. Our results suggest the new estimator should be used, in
particular, if substantial unobserved heterogeneity is present.
