# A D-vine copula based model for repeated measurements extending linear mixed models with homogeneous correlation structure

## TL;DR

This paper introduces a flexible D-vine copula-based model for unbalanced longitudinal data, extending linear mixed models by allowing arbitrary margins and complex dependence structures, with efficient estimation and better performance in real data.

## Contribution

It presents a novel D-vine copula approach for longitudinal data that handles missing values, offers a sequential estimation method, and improves predictive accuracy over traditional linear mixed models.

## Key findings

- Model outperforms linear mixed models in heart surgery data analysis
- Sequential estimation is validated through simulation
- Handles missing data without data discard

## Abstract

We propose a model for unbalanced longitudinal data, where the univariate margins can be selected arbitrarily and the dependence structure is described with the help of a D-vine copula. We show that our approach is an extremely flexible extension of the widely used linear mixed model if the correlation is homogeneous over the considered individuals. As an alternative to joint maximum-likelihood a sequential estimation approach for the D-vine copula is provided and validated in a simulation study. The model can handle missing values without being forced to discard data. Since conditional distributions are known analytically, we easily make predictions for future events. For model selection we adjust the Bayesian information criterion to our situation. In an application to heart surgery data our model performs clearly better than competing linear mixed models.