Approximate inference in latent variable models based on dimension-wise quadrature

Approximate methods are considered for likelihood inference to longitudinal and multidimensional data within the context of health science studies.The complexity of these data necessitates the use of sophisticated statistical models that can pose significant challenges for model fitting in termsof computational speed, memory storage, and accuracy of the estimates. Our methodology is motivated by a study that examines the temporal evolution of the mental status of the US elderly population between 2006 and 2010. We propose modeling the individual mental status as a latentprocess also accounting for the effects of individual specific characteristics, such as gender, age, and years of educational attainment. We describethe specification of such a model within the generalized linear latent variable framework, and its efficient estimation using a recent technique,called dimension-wise quadrature. The latter allows a fast and streamlined analytical approximate inference for complex models, with better orno degradation in accuracy compared with the standard techniques, such as Laplace approximation and adaptive quadrature. The model and themethod are applied in the analysis of cognitive assessment data from the health and retirement study combined with the asset and health dynamicstudy.