Flexible Modeling of Random Effects in Linear Mixed Models

Flexible modelling of random effects in linear mixed models has
attracted some attention recently. Following Verbeke and Lesaffre
(1996), we propose the use of finite skew-normal mixtures which
includes the finite normal mixtures as a special case and provides
flexibility in capturing a broad range of non-normal behavior,
controlled by a tuning parameter that controls the skewness of the
mixture components. Likelihood based inference is adopted since the
marginal likelihood may be expressed in closed form and an EM
algorithm for maximum likelihood estimation is developed which
results in an analytically tractable maximization step. In addition,
we offer a general information-based method for obtaining the
asymptotic covariance matrix of maximum likelihood estimates.
Numerical results on simulated and real data sets
are provided to demonstrate the usefulness of the proposed methodology.