Joint modeling of composite quantile regression for multiple ordinal longitudinal data with its applications to a dementia dataset

In the context of longitudinal data regression modeling, individuals often have two or more response indicators, and these response indicators are typically correlated to some extent. Additionally, in the field of clinical medicine, the response indicators of longitudinal data are often ordinal. For the joint modeling of multivariate ordinal longitudinal data, methods based on mean regression (MR) are commonly used to study latent variables. However, for data with non-normal errors, MR methods often perform poorly. As an alternative to MR methods, composite quantile regression (CQR) can overcome the limitations of MR methods and provide more robust estimates. This article proposes a joint relative composite quantile regression method (joint relative CQR) for multivariate ordinal longitudinal data and investigates its application to a set of longitudinal medical datasets on dementia. Firstly, the joint relative CQR method for multivariate ordinal longitudinal data is constructed based on the pseudo composite asymmetric Laplace distribution (PCALD) and latent variable models. Secondly, the parameter estimation problem of the model is studied using MCMC algorithms. Finally, Monte Carlo simulations and a set of longitudinal medical datasets on dementia validate the effectiveness of the proposed model and method.