Hwang Wen-Han, Heinze Dean, Stoklosa Jakub
Institute of Statistics, National Chung Hsing University, Taichung, Taiwan.
Research Centre of Applied Alpine Ecology, La Trobe University, Victoria, Australia.
Biom J. 2019 Jul;61(4):1073-1087. doi: 10.1002/bimj.201800328. Epub 2019 May 14.
Zero-truncated data arises in various disciplines where counts are observed but the zero count category cannot be observed during sampling. Maximum likelihood estimation can be used to model these data; however, due to its nonstandard form it cannot be easily implemented using well-known software packages, and additional programming is often required. Motivated by the Rao-Blackwell theorem, we develop a weighted partial likelihood approach to estimate model parameters for zero-truncated binomial and Poisson data. The resulting estimating function is equivalent to a weighted score function for standard count data models, and allows for applying readily available software. We evaluate the efficiency for this new approach and show that it performs almost as well as maximum likelihood estimation. The weighted partial likelihood approach is then extended to regression modelling and variable selection. We examine the performance of the proposed methods through simulation and present two case studies using real data.
零截断数据出现在各个学科中，在这些学科中，虽然观察到计数，但在抽样过程中无法观察到零计数类别。最大似然估计可用于对这些数据进行建模；然而，由于其非标准形式，使用知名软件包不容易实现，通常需要额外的编程。受罗伊 - 布莱克威尔定理的启发，我们开发了一种加权偏似然方法来估计零截断二项式和泊松数据的模型参数。由此产生的估计函数等同于标准计数数据模型的加权得分函数，并允许应用现成的软件。我们评估了这种新方法的效率，并表明它的性能几乎与最大似然估计一样好。然后将加权偏似然方法扩展到回归建模和变量选择。我们通过模拟检验了所提出方法的性能，并给出了两个使用实际数据的案例研究。
