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Linear Mixed-Effects Models for Non-Gaussian Continuous Repeated Measurement Data

Özgür Asar (Acibadem University)

We consider the analysis of continuous repeated measurement outcomes that are collected longitudinally. 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. To meet the computational challenges presented by large data-sets, i.e., in the current context, data-sets with many subjects and/or many repeated measurements per subject, we propose a novel implementation of maximum likelihood estimation using a computationally efficient sub-sampling-based 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 introduce 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.