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Title: Revisiting the mixture approach to mixed models: Thoughts on clustering and dimension reduction Authors:  Jochen Einbeck - Durham University (United Kingdom) [presenting]
Yingjuan Zhang - Durham University (United Kingdom)
Abstract: For generalized regression scenarios under various response distributions (Gaussian, Poisson, Binomial), the modern statistical methodology can deal with random effects on one or two levels quite easily. Such a methodology generally assumes a Gaussian distribution for the random effects, enabling access to tools such as the Laplace Approximation in order to integrate these out of the likelihood. An alternative, and less widely known approach, facilitates this integration step by means of a discrete mixture distribution based on a small number of mass points which can be estimated alongside with their masses and any regression parameters in a simple EM algorithm. We review this methodology with particular focus on its (not very widely appreciated) ability to cluster the units under investigation via the posterior probabilities of component membership resulting as a by-product from the EM algorithm. Several examples will be provided, including a case study involving the analysis of Covid-19 mortality rates. The extension of the methodology to multivariate response scenarios, where the random effect takes on the additional functionality of identifying a one-dimensional latent subspace approximating the original data, is discussed.