Count data sets are traditionally analyzed using the ordinary Poisson distribution. However, such a model has its applicability limited as it can be somewhat restrictive to handle specific data structures. In this case, it arises the need for obtaining alternative models that accommodate, for example, (a) zero-modification (inflation or deflation at the frequency of zeros), (b) overdispersion, and (c) individual heterogeneity arising from clustering or repeated (correlated) measurements made on the same subject. Cases (a)-(b) and (b)-(c) are often treated together in the statistical literature with several practical applications, but models supporting all at once are less common. Hence, this paper's primary goal was to jointly address these issues by deriving a mixed-effects regression model based on the hurdle version of the Poisson-Lindley distribution. In this framework, the zero-modification is incorporated by assuming that a binary probability model determines which outcomes are zero-valued, and a zero-truncated process is responsible for generating positive observations. Approximate posterior inferences for the model parameters were obtained from a fully Bayesian approach based on the Adaptive Metropolis algorithm. Intensive Monte Carlo simulation studies were performed to assess the empirical properties of the Bayesian estimators. The proposed model was considered for the analysis of a real data set, and its competitiveness regarding some well-established mixed-effects models for count data was evaluated. A sensitivity analysis to detect observations that may impact parameter estimates was performed based on standard divergence measures. The Bayesian p -value and the randomized quantile residuals were considered for model diagnostics.

中文翻译：

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用于分析零修正分层计数数据的新混合效应回归模型

计数数据集传统上使用普通泊松分布进行分析。然而，这种模型的适用性有限，因为它在处理特定数据结构时可能会有些限制。在这种情况下，需要获得替代模型来适应，例如，(a) 零修正（零频率下的通货膨胀或通货紧缩），(b) 过度分散，以及 (c) 由聚类或对同一主题进行的重复（相关）测量。案例 (a)-(b) 和 (b)-(c) 在统计文献中经常与几个实际应用一起处理，但同时支持所有这些的模型并不常见。因此，本文' 的主要目标是通过基于 Poisson-Lindley 分布的障碍版本推导出混合效应回归模型来共同解决这些问题。在此框架中，通过假设二元概率模型确定哪些结果为零值，并且零截断过程负责生成正观察，来合并零修改。从基于自适应大都会算法的完全贝叶斯方法获得模型参数的近似后验推断。进行了密集的蒙特卡罗模拟研究以评估贝叶斯估计量的经验特性。所提出的模型被考虑用于分析真实数据集，并评估了它在一些完善的计数数据混合效应模型方面的竞争力。基于标准的发散度量进行了灵敏度分析，以检测可能影响参数估计的观察结果。贝叶斯 p 值和随机分位数残差被考虑用于模型诊断。