Sufficient dimension reduction for clustered data via finite mixture modelling

IF 0.8 4区 数学 Q3 STATISTICS & PROBABILITY
F.K.C. Hui, L.H. Nghiem
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引用次数: 2

Abstract

Sufficient dimension reduction (SDR) is an attractive approach to regression modelling. However, despite its rich literature and growing popularity in application, surprisingly little research has been done on how to perform SDR for clustered data, for example as is commonly arises in longitudinal studies. Indeed, current popular SDR methods have been mostly based on a marginal estimating equation approach. In this article, we propose a new approach to SDR for clustered data based on a combination of finite mixture modelling and mixed effects regression. Finite mixture models offer a flexible means of estimating the fixed effects central subspace, based on slicing the space up and probabilistically clustering observations to each slice (mixture component). Dimension reduction is achieved by having the mixing proportions vary only through the sufficient fixed effect predictors. We then incorporate random effects as a natural means of accounting for correlations within clusters. We employ a Monte Carlo expectation–maximisation algorithm to estimate the model parameters and fixed effects central subspace, and discuss methods for associated uncertainty quantification and prediction. Simulation studies demonstrate that our approach performs strongly against both estimating equation methods for estimating the fixed effects central subspace, and SDR methods which do not account for within-cluster correlation. Finally, we apply the proposed approach to a data set on air pollutant monitoring across 13 stations in the Eastern United States.

通过有限混合模型对聚类数据进行足够的降维
充分降维(SDR)是一种有吸引力的回归建模方法。然而,尽管其文献丰富,应用日益普及,但令人惊讶的是,关于如何对聚类数据执行SDR的研究却很少,例如在纵向研究中常见的研究。事实上,目前流行的SDR方法大多基于边际估计方程方法。在本文中,我们提出了一种基于有限混合建模和混合效应回归相结合的聚类数据SDR新方法。有限混合模型提供了一种灵活的方法来估计固定效应的中心子空间,基于对空间的分割和对每个切片(混合分量)的概率聚类观察。只有通过足够的固定效应预测因子,混合比例才会发生变化,从而实现降维。然后,我们将随机效应作为计算集群内相关性的自然手段。我们采用蒙特卡罗期望最大化算法来估计模型参数和固定效应中心子空间,并讨论了相关的不确定性量化和预测方法。仿真研究表明,我们的方法对估计固定效应中心子空间的估计方程方法和不考虑簇内相关性的SDR方法都有很强的性能。最后,我们将提出的方法应用于美国东部13个站点的空气污染物监测数据集。
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来源期刊
Australian & New Zealand Journal of Statistics
Australian & New Zealand Journal of Statistics 数学-统计学与概率论
CiteScore
1.30
自引率
9.10%
发文量
31
审稿时长
>12 weeks
期刊介绍: The Australian & New Zealand Journal of Statistics is an international journal managed jointly by the Statistical Society of Australia and the New Zealand Statistical Association. Its purpose is to report significant and novel contributions in statistics, ranging across articles on statistical theory, methodology, applications and computing. The journal has a particular focus on statistical techniques that can be readily applied to real-world problems, and on application papers with an Australasian emphasis. Outstanding articles submitted to the journal may be selected as Discussion Papers, to be read at a meeting of either the Statistical Society of Australia or the New Zealand Statistical Association. The main body of the journal is divided into three sections. The Theory and Methods Section publishes papers containing original contributions to the theory and methodology of statistics, econometrics and probability, and seeks papers motivated by a real problem and which demonstrate the proposed theory or methodology in that situation. There is a strong preference for papers motivated by, and illustrated with, real data. The Applications Section publishes papers demonstrating applications of statistical techniques to problems faced by users of statistics in the sciences, government and industry. A particular focus is the application of newly developed statistical methodology to real data and the demonstration of better use of established statistical methodology in an area of application. It seeks to aid teachers of statistics by placing statistical methods in context. The Statistical Computing Section publishes papers containing new algorithms, code snippets, or software descriptions (for open source software only) which enhance the field through the application of computing. Preference is given to papers featuring publically available code and/or data, and to those motivated by statistical methods for practical problems.
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