Linear mixed effects models for non-Gaussian continuous repeated measurement data
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AbstractWe 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 that are 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 subsampling-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 reanalyse two data sets, from cystic fibrosis and nephrology research, that were previously analysed by using Gaussian linear mixed effects models.
CitationAsar, Ö., Bolin, D., Diggle, P. J., & Wallin, J. (2020). Linear mixed effects models for non-Gaussian continuous repeated measurement data. Journal of the Royal Statistical Society: Series C (Applied Statistics), 69(5), 1015–1065. doi:10.1111/rssc.12405
SponsorsThis work has been partially supported by the Swedish Research Council under grant 201604187. The authors are grateful for the valuable comments from reviewers and editors, which resulted in a much improved manuscript. We also thank Kristin Kirchner for helpful discussions regarding the Petrov–Galerkin method.
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