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Motivated by better modeling of intra-individual variability in longitudinaldata, we propose a class of location-scale mixed effects models, in which thedata of each individual is modeled by a parameter-varying generalizedhyperbolic distribution. We first study the local maximum-likelihoodasymptotics and reveal the instability in the numerical optimization of thelog-likelihood. Then, we construct an asymptotically efficient estimator basedon the Newton-Raphson method based on the original log-likelihood function withthe initial estimator being naive least-squares-type. Numerical experiments areconducted to show that the proposed one-step estimator is not onlytheoretically efficient but also numerically much more stable and much lesstime-consuming compared with the maximum-likelihood estimator.

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