Likelihood‐based inference for linear mixed‐effects models using the generalized hyperbolic distribution

Abstract

In this paper, we develop statistical methodology for the analysis of data under nonnormal distributions, in the context of mixed effects models. Although the multivariate normal distribution is useful in many cases, it is not appropriate, for instance, when the data come from skewed and/or heavy‐tailed distributions. To analyse data with these characteristics, in this paper, we extend the standard linear mixed effects model, considering the family of generalized hyperbolic distributions. We propose methods for statistical inference based on the likelihood function, and due to its complexity, the EM algorithm is used to find the maximum likelihood estimates with the standard errors and the exact likelihood value as a by‐product. We use simulations to investigate the asymptotic properties of the expectation‐maximization algorithm (EM) estimates and prediction accuracy. A real example is analysed, illustrating the usefulness of the proposed methods.