Department of Statistics, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran.
Department of Statistics, Faculty of Sciences, Imam Khomeini International University, Iran.
Biom J. 2022 Apr;64(4):758-770. doi: 10.1002/bimj.202100157. Epub 2022 Jan 5.
In employing spatial regression models for counts, we usually meet two issues. First, the possible inherent collinearity between covariates and the spatial effect could lead to misleading inferences. Second, real count data usually reveal over- or under-dispersion where the classical Poisson model is not appropriate to use. We propose a flexible Bayesian hierarchical modeling approach by joining nonconfounding spatial methodology and a newly reconsidered dispersed count modeling from the renewal theory to control the issues. Specifically, we extend the methodology for analyzing spatial count data based on the gamma distribution assumption for waiting times. The model can be formulated as a latent Gaussian model, and consequently, we can carry out the fast computation by using the integrated nested Laplace approximation method. We examine different popular approaches for handling spatial confounding and compare their performances in the presence of dispersion. Two real applications from a crime study against women in India as well as stomach cancer incidences in Slovenia motivate the suggested methods. We also perform a simulation study to understand the proposed approach's merits better. Supplementary Materials for this article are available.
在使用空间回归模型进行计数时，我们通常会遇到两个问题。首先，协变量和空间效应之间可能存在固有的共线性，这可能导致误导性的推断。其次，实际的计数数据通常会呈现过分散或欠分散，而经典的泊松模型不适合使用。我们提出了一种灵活的贝叶斯分层建模方法，将非混杂空间方法与从更新理论重新考虑的新离散计数建模相结合，以控制这些问题。具体来说，我们扩展了基于等待时间的伽马分布假设的空间计数数据分析方法。该模型可以表示为一个潜在的高斯模型，因此，我们可以通过使用集成嵌套拉普拉斯逼近方法进行快速计算。我们检查了处理空间混杂的不同流行方法，并比较了它们在存在分散时的性能。来自印度反对妇女犯罪研究和斯洛文尼亚胃癌发病率的两个实际应用案例激发了所建议的方法。我们还进行了模拟研究，以更好地了解所提出方法的优点。本文的补充材料可在网上获取。
