Observed heterogeneity in the capture-recapture problem

Abstract

The main goal of the thesis is to develop methods for modelling observed heterogeneity in capture-recapture data. We start by elaborating the logistic regression methods for capture-recapture problems with continuous covariates so that dependencies between registrations can be modelled. The current methods assume that the lists are independent at the individuals level. This restriction is inappropriate as some heterogeneity may still remain due to other unobservable variables, and this may in-turn induce some dependence between some of the lists. Another reason is that some registrations are inherently dependent and inclusion of covariates will not eliminate the dependence. The modelling of dependencies is accomplished through the use of the multinomial logit model.

We then propose an approach that relaxes the linear in the logit assumption of the multinomial logit model. The logistic function is often criticized as having an implicit shape unsuitable for capture-recapture. Here we essentially elaborate the multinomial logit model proposed for capture-recapture models with continuous covariates so that the covariates are not necessarily linear in the logits.

After presenting the approaches for analysing capture-recapture data incorporating continuous covariates, we then focus on implementing the parametric bootstrap for these models. It has already been discussed at length that the symmetric (or asymptotic) confidence intervals are inappropriate for capture-recapture studies. In the literature, it has been noted that, for virtually all models proposed in capture-recapture literature the distribution of the estimate of the population size is skewed. Several authors have used the non-parametric bootstrap in the presence of continuous covariates but this bootstrap method results in a variance estimate which is likely to be smaller than the true variance, because it conditions on being observed.

The rest of the thesis focuses on methods for analysing defective capture-recapture data. These data do not conform to one or more of the assumptions of capture-recapture models. We first we develop an approach for analysing capture-recapture data when some registrations do not collect data on a subset of the population. Notice that if some registrations do not measure certain individuals then those individuals have a zero probability of being in all lists, implying the usual capture-recapture approaches fail.

We then work on approaches of modelling capture-recapture data when some of the registration do not measure some covariates of heterogenous catchability. The goal is to utilize all variables of heterogenous catchability available as in some cases dropping them may induce an `all-list' interaction and thus invalidate results. We present the EM algorithm for analyzing such data when there are only categorical covariates and multiple imputation for problems with missing continuous (and categorical) covariates.