Grants and Contributions:

Grant or Award spanning more than one fiscal year. (2017-2018 to 2022-2023)

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.