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arXiv · 1804.02592

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

Özgür Asar·David Bolin·Peter J. Diggle·Jonas Wallin
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Abstract

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.

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Özgür Asar, David Bolin, Peter J. Diggle, Jonas Wallin. 2018-04-07. Linear Mixed-Effects Models for Non-Gaussian Repeated Measurement Data. https://arxiv.org/abs/1804.02592

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