Joint modeling approach with cholesky decomposition using the scale mixtures of normal distributions

Abstract

Longitudinal data processing is of significant interest for several fields, includ-ing biomedical and agronomic applications. To address this approach, severalmixed models have been introduced in the literature (as well as models basedon Generalized Estimating Equations, GEE), for example. These models usu-ally consider within-subject dependence by parameterizing the scatter matrixusing the modified Cholesky decomposition (MCD) or the alternative Choleskydecomposition (ACD). Traditional models often assume that errors follow anormal distribution. However, this assumption may not be valid for many prac-tical cases. Extensions based on the Student-tand Laplace distributions havebeen proposed, but they might be too restrictive due to the fixed parametricform. To address these limitations, this thesis presents a two new regressionmodels that assum that the errors are drawn from the family of scale mixturesof normal distributions, considering two different decomposition structures forthe scatter matrix. We develop maximum likelihood estimates for these modelsand compare it to similar models that assume different distributions, includ-ing the normal, Student-t, and Laplace models. A study using simulated datademonstrates that the proposed models are efficient compared to similar modelsand produces promising results for predicting new observations. Furthermore,the methodology is validated on real data, demonstrating good performance interms of estimation accuracy and robustness to outliers.