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Abstract:
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It is becoming increasingly common in longitudinal studies to collect and analyze data on multiple responses. For example, in the social sciences we may be interested in uncovering the factors driving mental health of individuals over time, where mental health is measured using a set of questionnaire items. One approach to analyzing such multi-dimensional data is to use multivariate mixed models, an extension of the standard univariate mixed model to handle multiple responses. Estimating a multivariate mixed model presents a considerable challenge however, let alone performing variable selection to uncover which covariates are important in driving each response. In this talk, motivated by composite likelihood ideas, we present a new method for estimation and fixed effects selection in multivariate mixed models, called Approximate Pairwise Likelihood Estimation and Shrinkage. The method works by constructing a quadratic approximation to each term in the pairwise likelihood function, and then augmenting this approximate pairwise likelihood with a penalty that encourages both individual and group coefficient sparsity. This leads to a relatively fast method of model selection,
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