A Study Of Latent Factor Model For Multivariate Longitudinal Data

In recent years,analysis of longitudinal data has become one of the hottest research topics in statistics.High dimensional longitudinal data are widely applied in many research fields,such as biology,medicine,economics,psychology and social sciences.In longitudinal data,some variables cannot be observed directly,we need more response variables to depict these latent factors,and repeated measurements can depict how these latent factors change over time.However,we are often interested in these latent factors and the relationship between them and covariates.In this paper,we review the research methods of longitudinal data,then we intro-duce and apply a latent factor linear mixed model to process high dimensional longitu-dinal data.This model combines the factor analysis model and the multivariate linear mixed model—the factor analysis model is used to reduce high dimensional response variables into low dimensional latent factors,the multivariate linear mixed model is used to study the correlation between latent factors and covariates.EM algorithm is used to obtain the estimates of model parameters.The dataset we used derives from CHARLS,aims to study the health status of the old people and the influence factors.Simulation study and real data study have evaluated the efficiency of the method.