Department of Economics, University of Perugia, 06123 Perugia, Italy.
Biometrics. 2024 Mar 27;80(2). doi: 10.1093/biomtc/ujae017.
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.
本文将刘等人提出的经验似然（EL）方法扩展到一种新的非常灵活的潜类模型家族，用于捕获-再捕获数据，也允许在前一次捕获历史的基础上，根据潜在类型和协变量进行序列依赖。EL 方法允许直接估计总体规模，而不是通过添加与协变量配置条件相关的估计值。本文提出了一种用于最大似然估计的 Fisher 评分算法，并引入了一种比传统 EL 方法更有效的估计非参数分量的替代方法；这使我们能够证明协变量的非参数分布与从未捕获的概率之间的映射是一一对应的，并且是严格递增的。概述了渐近结果，并提出了一种用于构建总体大小的轮廓似然置信区间的方法。基于真实数据的两个示例用于说明所提出的方法，模拟研究表明，在估计总体漏报时，这里提出的方法比基于条件最大似然估计的方法效率高得多，尤其是在样本量不够大时。
