Mixed-effects location-scale model based on generalized hyperbolic distribution

TL;DR

This paper introduces a novel mixed-effects location-scale model utilizing generalized hyperbolic distributions to better capture intra-individual variability in longitudinal data, with an efficient and stable estimation method.

Contribution

It develops a new class of models and an efficient estimation approach that improves stability and computational speed over traditional maximum-likelihood methods.

Findings

The proposed estimator is theoretically efficient.

The estimator is numerically stable and faster.

Numerical experiments validate the method's effectiveness.

Abstract

Motivated by better modeling of intra-individual variability in longitudinal data, we propose a class of location-scale mixed effects models, in which the data of each individual is modeled by a parameter-varying generalized hyperbolic distribution. We first study the local maximum-likelihood asymptotics and reveal the instability in the numerical optimization of the log-likelihood. Then, we construct an asymptotically efficient estimator based on the Newton-Raphson method based on the original log-likelihood function with the initial estimator being naive least-squares-type. Numerical experiments are conducted to show that the proposed one-step estimator is not only theoretically efficient but also numerically much more stable and much less time-consuming compared with the maximum-likelihood estimator.