标题： 建模共线性和空间相关数据 显示英文标题

标题： Modelling collinear and spatially correlated data

摘要： 在本工作中，我们提出了一种统计方法，在存在i)预测变量之间的高度相关性以及ii)响应变量的空间相关性的前提下，区分并解释多个预测变量与响应变量在小区域层面的复杂关系。高度相关的协变量在标准多重回归模型中会导致共线性问题。文献中已经提出了许多方法来解决这个问题。一种非常常见的方法是创建一个综合所有高度相关变量的指标。例如，众所周知，通过多重剥夺指数（IMD）测量的社会剥夺与空气污染之间存在关系；该指标随后被用作评估空气污染对健康结果（如呼吸系统住院或死亡率）影响的混杂因素。然而，更具有信息量的是具体查看 IMD 的各个领域及其与空气污染的关系，以更好地理解其在流行病学分析中的混杂作用。在本文中，我们说明如何使用轮廓回归来分解和分析 IMD 的各个领域与空气污染之间的复杂关系，轮廓回归是一种用于同时聚类响应变量和协变量的贝叶斯非参数模型。此外，我们包含了一个内在空间条件自回归（ICAR）项，以考虑响应变量的空间相关性。 显示英文摘要

摘要： In this work we present a statistical approach to distinguish and interpret the complex relationship between several predictors and a response variable at the small area level, in the presence of i) high correlation between the predictors and ii) spatial correlation for the response. Covariates which are highly correlated create collinearity problems when used in a standard multiple regression model. Many methods have been proposed in the literature to address this issue. A very common approach is to create an index which aggregates all the highly correlated variables of interest. For example, it is well known that there is a relationship between social deprivation measured through the Multiple Deprivation Index (IMD) and air pollution; this index is then used as a confounder in assessing the effect of air pollution on health outcomes (e.g. respiratory hospital admissions or mortality). However it would be more informative to look specifically at each domain of the IMD and at its relationship with air pollution to better understand its role as a confounder in the epidemiological analyses. In this paper we illustrate how the complex relationships between the domains of IMD and air pollution can be deconstructed and analysed using profile regression, a Bayesian non-parametric model for clustering responses and covariates simultaneously. Moreover, we include an intrinsic spatial conditional autoregressive (ICAR) term to account for the spatial correlation of the response variable.