A Generalization of Chao%26apos;s Estimator for Covariate Information

作者：Boehning Dankmar; Vidal Diez Alberto; Lerdsuwansri Rattana; Viwatwongkasem Chukiat; Arnold Mark

来源：Biometrics, 2013, 69(4): 1033-1042.

DOI：10.1111/biom.12082

• Bias reduction
• Chao%26apos
• s estimator
• Closed capture-recapture
• Covariate modelling

This note generalizes Chao%26apos;s estimator of population size for closed capture-recapture studies if covariates are available. Chao%26apos;s estimator was developed under unobserved heterogeneity in which case it represents a lower bound of the population size. If observed heterogeneity is available in form of covariates we show how this information can be used to reduce the bias of Chao%26apos;s estimator. The key element in this development is the understanding and placement of Chao%26apos;s estimator in a truncated Poisson likelihood. It is shown that a truncated Poisson likelihood (with log-link) with all counts truncated besides ones and twos is equivalent to a binomial likelihood (with logit-link). This enables the development of a generalized Chao estimator as the estimated, expected value of the frequency of zero counts under a truncated (all counts truncated except ones and twos) Poisson regression model. If the regression model accounts for the heterogeneity entirely, the generalized Chao estimator is asymptotically unbiased. A simulation study illustrates the potential in gain of bias reduction. Comparisons of the generalized Chao estimator with the homogeneous zero-truncated Poisson regression approach are supplied as well. The method is applied to a surveillance study on the completeness of farm submissions in Great Britain.

• 出版日期2013-12