  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.
