Estimation of covariate effects in generalized linear mixed models with a misspecified distribution of random intercepts and slopes
Article first published online: 2 DEC 2012
Copyright © 2012 John Wiley & Sons, Ltd.
Statistics in Medicine
Volume 32, Issue 14, pages 2419–2429, 30 June 2013
How to Cite
Neuhaus, J. M., McCulloch, C. E. and Boylan, R. (2013), Estimation of covariate effects in generalized linear mixed models with a misspecified distribution of random intercepts and slopes. Statist. Med., 32: 2419–2429. doi: 10.1002/sim.5682
- Issue published online: 4 JUN 2013
- Article first published online: 2 DEC 2012
- Manuscript Accepted: 11 OCT 2012
- Manuscript Received: 27 JAN 2012
- generalized linear mixed models;
- Kullback–Leibler divergence;
- misspecified mixing distributions
Generalized linear mixed models with random intercepts and slopes provide useful analyses of clustered and longitudinal data and typically require the specification of the distribution of the random effects. Previous work for models with only random intercepts has shown that misspecifying the shape of this distribution may bias estimates of the intercept, but typically leads to little bias in estimates of covariate effects. Very few papers have examined the effects of misspecifying the joint distribution of random intercepts and slopes. However, simulation results in a recent paper suggest that misspecifying the shape of the random slope distribution can yield severely biased estimates of all model parameters. Using analytic results, simulation studies and fits to example data, this paper examines the bias in parameter estimates due to misspecification of the shape of the joint distribution of random intercepts and slopes. Consistent with results for models with only random intercepts, and contrary to the claims of severe bias in a recent paper, we show that misspecification of the joint distribution typically yields little bias in estimates of covariate effects and is restricted to covariates associated with the misspecified random effects distributions. We also show that misspecification of the distribution of random effects has little effect on confidence interval performance. Coverage rates based on the model-based standard errors from fitted likelihoods were generally quite close to nominal. Copyright © 2012 John Wiley & Sons, Ltd.