jmcm: An R Package for Joint Mean-Covariance Modeling of Longitudinal Data

Longitudinal studies commonly arise in various fields such as psychology, social science, economics and medical research, etc. It is of great importance to understand the dynamics in the mean function, covariance and/or correlation matrices of repeated measurements. However, high-dimensionality (HD) and positive-definiteness (PD) constraints are two major stumbling blocks in modeling of covariance and correlation matrices. It is evident that Cholesky-type decomposition based methods are effective in dealing with HD and PD problems, but those methods were not implemented in statistical software yet, causing a difficulty for practitioners to use. In this paper, we first introduce recently
developed Cholesky decomposition based methods for joint modeling of mean and covariance structures, namely modified Cholesky decomposition (MCD), alternative Cholesky decomposition (ACD) and hyperspherical parameterization of Cholesky factor (HPC). We then introduce our newly developed R package jmcm which is currently able to handle longitudinal data that follows a Gaussian distribution using the MCD, ACD and HPC methods. The use of package jmcm is illustrated and a comparison of those methods is made through the analysis of two real data sets.