  We consider the analysis of continuous repeated measurement outcomes that are
collected through time, also known as longitudinal data. A standard framework
for analysing data of this kind is a linear Gaussian mixed-effects model within
which the outcome variable can be decomposed into fixed-effects, time-invariant
and time-varying random-effects, and measurement noise. We develop methodology
that, for the first time, allows any combination of these stochastic components
to be non-Gaussian, using multivariate Normal variance-mean mixtures. We
estimate parameters by max- imum likelihood, implemented with a novel,
computationally efficient stochastic gradient algorithm. We obtain standard
error estimates by inverting the observed Fisher-information matrix, and obtain
the predictive distributions for the random-effects in both filtering
(conditioning on past and current data) and smoothing (conditioning on all
data) contexts. To implement these procedures, we intro- duce an R package,
ngme. We re-analyse two data-sets, from cystic fibrosis and nephrology
research, that were previously analysed using Gaussian linear mixed effects
models.
