Mixed Model Selection: Theory and Application

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。本研究的重点将是研究渐近性质和有限样本的程序，其中包括比较常用的特设方法的性能。该研究还将开发应用程序的选择方法选择因素的纵向数据，基因筛选相关的数量性状的兴趣，并在小面积估计问题的调查模型选择的基因。此外，将通过开发免费软件提供所开发的方法。该研究还将改进研究人员最近完成的工作，其中建立了线性混合模型中一致因子选择的条件。这些改进将包括开发一种更有效的线性混合模型选择方法，并研究一些自适应程序。线性和广义线性混合模型是一类重要的模型，允许放松标准假设，如独立性或方差齐性的观察，并考虑到更复杂的数据结构，在相当一般的方式。典型的应用包括随着时间的推移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理和预测来说是很重要的，但是很少有人正式研究这个问题。本研究试图填补这一重要的空白，从理论的角度开发新的程序，正确的因素选择，并通过广泛的模拟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的环境中，包括纵向数据，遗传筛查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.