Estimating the size of a closed population by modeling latent and observed heterogeneity.

IF 1.4 4区 数学 Q3 BIOLOGY
Biometrics Pub Date : 2024-03-27 DOI:10.1093/biomtc/ujae017
Francesco Bartolucci, Antonio Forcina
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引用次数: 0

Abstract

The paper extends the empirical likelihood (EL) approach of Liu et al. to a new and very flexible family of latent class models for capture-recapture data also allowing for serial dependence on previous capture history, conditionally on latent type and covariates. The EL approach allows to estimate the overall population size directly rather than by adding estimates conditional to covariate configurations. A Fisher-scoring algorithm for maximum likelihood estimation is proposed and a more efficient alternative to the traditional EL approach for estimating the non-parametric component is introduced; this allows us to show that the mapping between the non-parametric distribution of the covariates and the probabilities of being never captured is one-to-one and strictly increasing. Asymptotic results are outlined, and a procedure for constructing profile likelihood confidence intervals for the population size is presented. Two examples based on real data are used to illustrate the proposed approach and a simulation study indicates that, when estimating the overall undercount, the method proposed here is substantially more efficient than the one based on conditional maximum likelihood estimation, especially when the sample size is not sufficiently large.

通过对潜在和观察到的异质性建模来估算封闭种群的规模。
本文将 Liu 等人的经验似然法(EL)扩展到一个新的、非常灵活的捕获-再捕获数据的潜类模型系列,该模型还允许对先前捕获历史的序列依赖,并以潜类和协变量为条件。EL 方法允许直接估计总体种群数量,而不是通过添加协变量配置条件下的估计值。我们提出了最大似然估计的费雪评分算法,并引入了一种更有效的替代传统 EL 方法的方法来估计非参数成分;这使我们能够证明协变量的非参数分布与从未被捕获的概率之间的映射是一一对应且严格递增的。概述了渐近结果,并介绍了构建人口规模的轮廓似然置信区间的程序。模拟研究表明,在估算总体少计人数时,本文提出的方法比基于条件最大似然估算的方法更有效,尤其是在样本量不够大的情况下。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Biometrics
Biometrics 生物-生物学
CiteScore
2.70
自引率
5.30%
发文量
178
审稿时长
4-8 weeks
期刊介绍: The International Biometric Society is an international society promoting the development and application of statistical and mathematical theory and methods in the biosciences, including agriculture, biomedical science and public health, ecology, environmental sciences, forestry, and allied disciplines. The Society welcomes as members statisticians, mathematicians, biological scientists, and others devoted to interdisciplinary efforts in advancing the collection and interpretation of information in the biosciences. The Society sponsors the biennial International Biometric Conference, held in sites throughout the world; through its National Groups and Regions, it also Society sponsors regional and local meetings.
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