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Modelling longitudinal data through matrix-variate normal mixtures

Last modified: 2013-06-14

#### Abstract

Multivariate longitudinal data occur when various attributes are measured on a sample of statistical units at different times. The collected data can be arranged in a three-way data structure characterized by rows (i.e. the statistical units),columns (i.e. the different times/occasions) and layers (i.e. the attributes). In this perspective, each observed statistical unit is a matrix of observations instead of the conventional p-dimensional vector. Clustering observational matrix units by means of a special mixture model is proposed. An explicit assumption of this approach is that the total variability arises from the compound of the ’within’ variability of the attributes and the variability ’between’ the different times, which explicitly accounts for the relationship between measurements at different time points through a modified Cholesky decomposition. The effectiveness of the proposed method is illustrated on longitudinal data from the Health and Retirement Study (HRS) study.

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