High-dimensional Longitudinal Data Clustering Analysis Based On Latent Variable Linear Mixed Model

Longitudinal data depicts the dynamic relationship between different research subjects in time or space,and is widely used in various fields including medicine,economics,social and behavioral sciences.With the development of technology,high-dimensional longitudinal data modeling has become one of the hot research topics in various fields.Linear hybrid models are often used to study longitudinal data,which consider the impact of individual effects on the overall population and the correlation of multiple observations in the same body.It is often assumed in linear hybrid models Random effects independently follow the same normal distribution,but there is a clustering effect between the individuals we observed and studied,that is,there is heterogeneity in the longitudinal data,and the original distribution assumptions cannot meet our modeling needs.In this regard,this paper discusses a latent linear mixture model based on Gaussian mixture distribution,which is a combination of mixed factor model and multiple linear mixture model.The mixed factor model in this paper uses the factor analysis model to reduce the dimensionality of high-dimensional response variables to low-dimensional potential factors,while using the Gaussian mixture model to cluster the study individuals.The multivariate linear mixed model is used to study the longitudinal trend between the potential factors of each subgroup,that is,not only to explore the development trend of latent variables over time,but also to evaluate the factors affecting the development of latent variables and the correlation between potential factors.In this paper,the EM algorithm is used to estimate the relevant parameters,and the number of clusters is determined according to the BIC criterion,and the numerical simulation shows that the EM algorithm has a good estimation effect on the parameter estimation of the model.Finally,we conduct cluster analysis of listed logistics enterprises based on the financial index data,and study the development factors affecting corporate profitability,operation,growth and debt servicing,and analyze the correlation between these four indicators.