On discrimination in multivariate repeated measures data

该研究计划的重点是在多变量重复测量（MRM）设计中预测组成员资格的准确分类模型的开发。新兴技术正在提供对多个学科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，其特征在于非高斯连续分布和复杂的相关结构。重复测量判别分析（RMDA）已被提出用于预测多变量重复测量设计中的组成员资格，其中多个结果在两个或多个场合被重复测量。但是，这些程序可能并不总是产生最佳的分类精度在重复测量研究与小样本量的特点是非高斯结果分布（例如，多元偏态正态分布和多元t分布）和高维数据。因此，对MRM中的精确预测模型的需求增加。本研究计划的首要目的是开发更准确的分类模型，用于区分以偏态或重尾分布为特征的多变量重复测量设计中的人群。这项研究有以下两个主要目标。*1.将开发基于判别分析和二次推理函数（QIF）的鲁棒分类器，用于非高斯分布的MRM设计中的预测。将使用最大加权似然（MWL）和经验似然（EL）估计量来推导稳健的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的错误率。2.当预测非高斯MRM数据中的组成员关系时，将基于RMDA和QIF分类器的EL和MWL估计开发拟合优度检验。3.长期的研究目标将调查变量选择技术，选择结果和/或重复测量，最具歧视性的权力，以获得有效的RMDA和QIF分类器在多变量重复测量设计。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。这项研究的成果将包括强大的分类模型，可用于预测MRM设计和相应的统计软件包，以实现其使用的组成员。该研究将有助于重复测量数据分类模型的统计科学。最后，该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，从而使他们在统计学方面取得成功。

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.