Mixture models in capture-recapture studies
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(Published version)
Date
2009
Authors
Thandrayen, Joanne
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thesis
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Abstract
The estimation of human population size is important for decision making and planning. It is not uncommon that statistical techniques are employed towards this purpose. A recent advance in the counting of missing human populations is the capture-recapture approach which utilizes duplicate information from several incomplete lists to estimate the number of people otherwise unobserved. Capture-recapture methods originated in the estimation of animal populations in wildlife biology, and have been widely used to count hidden or hard-to-reach populations in the areas of epidemiology and public health. The use of multiple lists gives rise to two main issues in the capture-recapture framework, namely list dependence and heterogeneity; the latter problem can be further classified as observed and unobserved heterogeneity. The literature is well developed when it concerns separately modelling these problems. However, we believe that the literature can still be improved when it comes to a joint modelling of these problems. This thesis provides some methods which can simultaneously control the effects due to list dependence and heterogeneity. First, we introduce a binomial latent model which focuses on the heterogeneity aspect and use covariates to control the observed heterogeneity within capture-recapture data; the unobserved heterogeneity is accounted for by means of latent classes. The covariates effects can be modelled either in the latent class probabilities or the capture probabilities. In this particular approach, the modelling is designed so that the covariates affect the latent class probabilities. We then extend this approach to include list dependence by employing a multinomial latent class model in which the lists effects are incorporated within the capture probabilities. Second, we start with a model which can account for list dependence and unobserved heterogeneity by means of multinomial latent class modelling.
Similarly, the lists effects are modelled in the capture probabilities. We then extend the model to include the covariates effects. Here, the modelling is set up in such a way that the covariates affect the capture probabilities. This is thus an alternative methodology to the one above where we use the covariates within the latent classes. It is to be noted that our modelling can involve both discrete and continuous covariates and this is a significant benefit of our methods. We employ the maximum likelihood estimation technique and the Expectation-Maximization (EM) algorithm for maximization purposes. We work with the conditional likelihood function which has the advantage that it can perform estimation based only on the captured individuals and does not require information about the whole population. This is particulary suitable when covariate modelling is involved as the covariate information for the uncaptured individuals is not available. At the same time, this advantage allows the conditional likelihood approach to be computationally less tedious than the full likelihood approach when it comes to running the EM algorithm. The difficulty of standard errors computations in latent class modelling is overcome by using an approximation to the observed Information matrix rather than directly evaluating the Information matrix. The methods are illustrated by means of both simulations and real examples concerning the undercount of homeless people in a city in Australia and diabetes patients in a town in Italy.
School/Discipline
School of Mathematics and Statistics
Dissertation Note
Thesis (PhD)--University of South Australia, 2009
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Copyright 2009 M. N. Joanne Thandrayen
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EN-AUS
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