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Abstract:
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Multiple sources and studies are widely available in various areas of science, and it is important to appropriately combine information from them to produce accurate and general statistical results. Multi-study factor analysis is a novel statistical framework that integrates several studies but is limited to continuous responses. Multivariate count data frequently occur in many applications, but modeling multivariate count data necessitates different statistical methodologies from continuous data. Some modeling approaches for multivariate count data, such as Poisson or negative binomial factor models, are available separately to each study or a single dataset after stacking them. However, they fail to simultaneously capture cross-study latent factor structures. This paper proposes a new modeling strategy for the joint analysis of multiple studies for multivariate count data to uncover common factors shared across studies and study-specific factors. Computationally, we propose a variational approximation method to estimate common and study-specific factor loadings. The proposed methods are illustrated in extensive simulations and real applications to dietary data.
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