Latent Factor Linear Mixed Model for High-Dimensional Clustered Data

• Activity Number: 27
• Type: Contributed
• Date/Time: Sunday, July 31, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Qing Yang*+ and Xinming An
• Companies: University of California at Los Angeles and University of California at Los Angeles
• Keywords: factor analysis ; linear mixed model ; high dimensional longitudinal data ; EM algorithm

Abstract

Linear mixed models have been widely used to analyze correlated longitudinal data. However, traditional linear mixed model can only handle repeated measurements for one single response. In practice, for many social and biomedical researchers, the interested quantities, such as depression and personality, cannot be observed or quantified directly. Multiple responses from questionnaires are often used to characterize these quantities, which will lead to high dimensional longitudinal data. In this paper we propose a latent factor linear mixed model for analyzing this type of data. It's a combination of factor analysis and multivariate linear mixed model. The high dimensional responses are reduced to low dimensional latent factors by using factor analysis model. Then multivariate linear mixed model is used to study the effects of covariates on the latent factors. When all latent variables have linear trends in time, we can use this model to access the relationship between the latent variables, which is of great interest in practice. An EM algorithm is developed to estimate the model. Simulation studies are used to investigate the computational properties of the EM algorithm.