Response Variable Is Continuous And Multisection Type Of Multivariate Longitudinal Data Analysis

Multiple longitudinal data refers to a group of data which is got from repeated measurements of several response variables of a unit. Such repeated measurements are taken at different times. There may be a cross-sectional correlation among the response variables. Measuring each response variable repeatedly, there may be a longitudinal correlation. Therefore, it is necessary to think about both the cross-sectional and the longitudinal correlation when analyzing multiple longitudinal data. Researchers earlier always regarded the outcomes measured at different times of each response variable of a unit as different time series, and created time series models. It neglected the cross-sectional correlation among the response variables and loss much information. Since J. Roy & X. Lin created a united model to fit multiple longitudinal data in 2000, scholars had a new understanding in its modeling way. R. V. Gueorguieva & G. Sanacora show that modeling united was better than modeling separately in their research in 2006.In addition, the response variables of a unit may be all continuous, or all discrete, or both of them. So, considering these qualities and modeling united is the key to analyze multiple longitudinal data. In recent years, researchers at home and abroad got a certain development of multiple longitudinal data in theory and practice. From modeling separately to modeling united, from"Analysis of multiple longitudinal data"to"Analysis of multiple longitudinal data under first-order autoregressive", then to"Analysis of multiple longitudinal outcomes with non-ignorable dropout", and"Analysis of discrete and continuous multiple longitudinal data", and so on. Researching on multiple longitudinal data is getting deeper and deeper.On the basis of previous research, the author of this thesis has read a lot of related references, job done as follow: Firstly, introducing the modeling process of multiple longitudinal data under first-order autoregressive made by Yan-Chun Xing in reference [1], and after introducing the certification of model fitting"First-order autoregressive among latent variables", the author of this thesis gives another proving way which is easier than the original. Secondly, on the basis of the reference [1], for a kind of complex multiple longitudinal data——"there is a first-order autoregressive among latent variables, response variables have both continuous variables and polytomous variables". The author of this thesis gives the modeling way and parameter estimation method. The job done by the author of this thesis promotes and enriches the theoretical research on multiple longitudinal data. At the same time, it has a certain role in guiding practice.