Mixed Model Selection: Theory and Application

[摘要]pi: Jiang/ rao本研究涉及线性和广义线性混合模型的模型选择程序的开发。本研究的重点是研究程序的渐近性质和有限样本性能，其中包括与常用的特设方法的比较。研究还将开发选择方法的应用，以选择纵向数据中的因素，与感兴趣的数量性状有关的基因的遗传筛选，以及从调查中获得的小区域估计问题的模型选择。此外，所开发的方法将通过开发免费软件提供。该研究还将改进研究者最近完成的工作，其中建立了线性混合模型中一致因素选择的条件。这些改进将包括开发更有效的线性混合模型选择方法，以及研究一些自适应过程。线性和广义线性混合模型是一类重要的模型，它们允许放松标准假设，如观测方差的独立性或同质性，并以相当一般的方式考虑更复杂的数据结构。典型的应用包括在一段时间内对患者进行重复测量或筛选可能与感兴趣的数量性状相关的候选基因。选择哪些因素应该或不应该出现在模型中对于模型推断和预测非常重要，但很少有人正式研究这个问题。本研究试图填补这一重要空白，从理论角度开发正确因素选择的新程序，并通过广泛的模拟来评估现实世界的表现。本研究的另一个重要组成部分是将其应用于各种现实世界环境，包括纵向数据，遗传筛选和调查抽样中的小面积估计。

AbstractDMS-0203676 & 0203724PIs: Jiang/RaoThis research involves development of model selection procedures for linear and generalized linear mixed models. The focus of this research will be on studying asymptotic properties and finite sample performance of the procedures, which will include comparisons to commonly used ad hoc methods. The research will also develop applications of the selection methodology to selecting factors in longitudinal data, genetic screening of genes related to quantitative traits of interest, and to model selection in small area estimation problems from surveys. In addition, the methods developed will be made accessible through the development of freely available software. The research will also improve work recently completed by the investigators where the conditions for consistent factor selection in linear mixed models were established. These improvements will include developing a more efficient method for linear mixed model selection, and studying some adaptive procedures. Linear and generalized linear mixed models are important classes of models which allow relaxation of standard assumptions like independence or homogeneity of variances of observations, and take into account more complicated data structures in quite general ways. Typical applications include repeated measurements made on a patient over time or screening of candidate genes that might be related to a quantitative trait of interest. Selecting which factors should or should not be in the model can be of importance for model inference and predictions, yet little if anything has been developed to formally study this problem. This research attempts to fill this important gap in the field of developing new procedures for correct factor selection from a theoretical perspective, and evaluating real-world performance via extensive simulations. Another important component of this research is to apply it in a variety of real-world settings including longitudinal data, genetic screening, and small area estimation in survey sampling.