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• Topic: Random effects model-based sufficient dimension reduction for independent clustered data
• Presenter: Dr. Linh Nghiem, University of Sydney
• Time: 10:00 AM (Vietnam), Monday, Dec 01, 2025
• Location: Room B1-1001, 279 Nguyen Tri Phuong St, Dien Hong Ward, HCMC

Abstract:

Sufficient dimension reduction (SDR) is a popular class of regression methods which aim to find a small number of linear combinations of covariates that capture all the information of the responses i.e., a central subspace. The majority of current methods for SDR focus on the setting of independent observations, while the few techniques that have been developed for clustered data assume the linear transformation is identical across clusters. We introduce random effects SDR, where cluster-specific random effect central subspaces are assumed to follow a distribution on the Grassmann manifold, and the random effects distribution is characterized by a covariance matrix on a tangent space. We incorporate random effect SDR within model-based inverse regression frameworks that can handle mixed types of predictors (time-variant/time-invariant, continuous/binary). A two-stage algorithm is proposed to estimate the overall fixed effect central subspace, and predict the cluster-specific random effect central subspaces. We demonstrate the consistency of the proposed estimators, while simulation studies demonstrate the superior performance of the proposed approach compared to global and cluster-specific SDR approaches. Finally, we apply the method to study the longitudinal association between the life expectancy of women and socioeconomic variables across 117 countries from 1990-2015. This is a joint work with Francis K.C.Hui at the Australian National University.

About presenter:

Linh Nghiem is currently a Lecturer in Statistics (promoted to Senior Lecturer from 2026) at the University of Sydney (Usyd). As a methodological and applied statistician, Linh is interested in developing novel statistical methodologies for complex settings to address scientific questions using data. His current interests are measurement error models, dimension reduction, and graphical models. His work has been published in the most globally prestigious statistical journals, including Biometrika, Journal of American Statistical Association, Biometrics, and Statistica Sinica. As an efficient teacher, Linh was awarded Early Career Teacher of the Year 2024 in the Faculty of Science at Usyd.

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