On discrimination in multivariate repeated measures data

多元重复测量数据中的歧视

• 批准号: RGPIN-2017-05869
• 负责人: Sajobi, Tolulope
• 金额: $ 1.02万
• 依托单位: University of Calgary
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=675424
• 关键词: discrimination; multivariate; repeated; measures; data

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.

本研究计划的重点是发展准确的分类模型，以预测多元重复测量（MRM）设计中的群体成员。新兴技术正在为多个学科的多个结果提供常规的重复测量收集。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的复杂数据，具有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群体成员，其中多个结果在两次或更多次重复测量。但是，在以非高斯结果分布（例如，多元偏态正态分布和多元t分布）和高维数据为特征的小样本量重复测量研究中，这些程序可能并不总是产生最佳的分类准确性。因此，在MRM中对准确的预测模型的需求越来越大。本研究计划的总体目的是开发更准确的分类模型，用于在以偏态或重尾分布为特征的多变量重复测量设计中区分人群群体。本研究有以下两个主要目的。* * * * * * 1。基于判别分析和二次推理函数（QIF）的鲁棒分类器将被开发用于非高斯分布的MRM设计的预测。最大加权似然（MWL）和经验似然（EL）估计器将用于导出稳健的RMDA和QIF分类器。比较这些分类器的性能指标将是自举交叉验证错误率。* * * * * * 2。在预测非高斯MRM数据的群体隶属性时，将基于RMDA和QIF分类器的EL和MWL估计开发拟合优度检验。* * * * * * 3。长期研究目标将研究变量选择技术，用于选择结果和/或具有最具歧视性的重复测量，以在多变量重复测量设计中获得有效的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。******本研究的结果将包括稳健的分类模型，可用于预测MRM设计中的群体成员和相应的统计软件包来实现它们的使用。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，这个研究项目为本科生和研究生提供了大量参与统计研究的培训机会，从而使他们在统计领域取得成功。