Multivariate Robust Linear Models for Multivariate Longitudinal Data

Linear models commonly used in longitudinal data analysis often assume a multivariate normal distribution. This assumption, however, can lead to biased mean parameter estimates in the presence of outliers. To address this, alternative linear models based on multivariate t distributions have been developed. In this paper, we review the commonly used multivariate distributions applicable to multivariate longitudinal data and introduce multivariate Laplace linear models (MLLMs) that are designed to handle outliers effectively. These models incorporate a scale matrix that is autoregressive, heteroscedastic, and positive definite, using modified Cholesky and hypersphere decompositions. We conduct simulation studies and apply these models to a real data example, comparing the performance of MLLMs with multivariate normal linear models (MNLMs) and multivariate t linear models (MTLMs), and providing insights on when each model is most appropriate.