On discrimination in multivariate repeated measures data

这项研究计划致力于开发准确的分类模型，用于预测多变量重复测量(MRM)设计中的组成员。新兴技术正在提供对几个学科的多个结果的重复测量的常规收集。然而，多变量重复测量数据的分析并不简单，因为它们通常是高维和复杂的数据，具有非高斯连续分布和复杂的相关性结构的特点。重复测量判别分析(RMDA)已被提出用于在多变量重复测量设计中预测组成员，其中多个结果在两个或更多情况下被重复测量。但是，在以非高斯结果分布(例如，多变量偏态正态分布和多变量t分布)和高维数据为特征的小样本重复测量研究中，这些方法可能并不总是产生最佳的分类精度。因此，在MRM中对准确的预测模型的需求一直在增加。这项研究的主要目的是开发更准确的分类模型，用于区分以偏态分布或重尾分布为特征的多变量重复测量设计中的总体组。这项研究有以下两个主要目标。 1.基于判别分析和二次推理函数(QIF)的稳健分类器将被开发用于非高斯分布特征的MRM设计的预测。最大加权似然(MWL)和经验似然(EL)估计器将被用来得到稳健的RMDA和QIF分类器。比较这些分类器的性能指标将是引导交叉验证错误率。 2.在预测非高斯MRM数据中的组成员时，将开发基于EL和MWL估计的RMDA和QIF分类器的拟合优度测试。 3.长期的研究目标是研究用于选择结果和/或具有最大区分力的重复测量的变量选择技术，以在多变量重复测量设计中得出有效的RMDA和QIF分类器。这些方法包括逐步重复测量、多变量方差分析和惩罚变量选择方法。 这项研究的结果将包括在MRM设计中可用于预测群体成员资格的稳健分类模型，以及实现其使用的相应统计程序包。本研究将有助于重复测量数据分类模型的统计科学研究。最后，这项研究计划为本科生和研究生提供了大量参与统计研究的培训机会，从而在统计学领域取得成功。

This program of research focuses on the development of accurate classification models for predicting group membership in multivariate repeated measures (MRM) designs. Emerging technologies are offering routine collection of repeated measurements on multiple outcomes in several disciplines. However, the analysis of multivariate repeated measures data are not straightforward, as they are usually high-dimensional and complex data, characterized by non-Gaussian continuous distributions and complex correlation structures. Repeated measures discriminant analysis (RMDA) have been proposed for predicting group membership in multivariate repeated measures designs in which multiple outcomes are repeatedly measured at two or more occasions. But these procedures may not always yield optimal classification accuracy in repeated measures studies with small sample sizes characterized by non-Gaussian outcome distributions (e.g., multivariate skewed normal and multivariate t distributions) and high-dimensional data. Accordingly, there has been an increased demand for accurate prediction models in MRM. This overarching purpose of this research program is to develop more accurate classification models for discriminating between population groups in multivariate repeated measures designs characterized by skewed or heavy-tailed distributions. This study has the following two main objectives. 1. Robust classifiers based on discriminant analysis and quadratic inference functions (QIF) will be developed for prediction in MRM designs characterized by non-Gaussian distributions. Maximum weighted likelihood (MWL) and empirical likelihood (EL) estimators will be used to derive robust RMDA and QIF classifiers. The performance metric to compare these classifiers will be the bootstrap cross-validated error rate. 2. Goodness-of-fit tests will be developed based on EL and MWL estimation for RMDA and QIF classifiers when predicting group membership in non-Gaussian MRM data. 3. The long-term research goal will investigate variable selection techniques for selecting outcomes and/or repeated measurements with the most discriminatory power to derive efficient RMDA and QIF classifiers in multivariate repeated measures designs. These include stepwise repeated measures multivariate analysis of variance and penalized variable selection approaches. The outcomes of this research will include robust classification models that can be adopted for predicting group membership in MRM design and corresponding statistical packages to implement their use. This research will contribute to the statistical science of classification models for repeated measures data. Finally, this research program abounds with training opportunities for undergraduate and graduate students to be involved in statistical research, leading to successful careers in statistics.