Prediction of Random Effects in Linear and Generalized Linear Models under Model Misspecification
Article first published online: 28 MAY 2010
© 2010, The International Biometric Society
Volume 67, Issue 1, pages 270–279, March 2011
How to Cite
McCulloch, C. E. and Neuhaus, J. M. (2011), Prediction of Random Effects in Linear and Generalized Linear Models under Model Misspecification. Biometrics, 67: 270–279. doi: 10.1111/j.1541-0420.2010.01435.x
- Issue published online: 14 MAR 2011
- Article first published online: 28 MAY 2010
- Received March 2009. Revised February 2010. Accepted March 2010.
- Mean square error of prediction;
- Mixture distribution;
Summary Statistical models that include random effects are commonly used to analyze longitudinal and correlated data, often with the assumption that the random effects follow a Gaussian distribution. Via theoretical and numerical calculations and simulation, we investigate the impact of misspecification of this distribution on both how well the predicted values recover the true underlying distribution and the accuracy of prediction of the realized values of the random effects. We show that, although the predicted values can vary with the assumed distribution, the prediction accuracy, as measured by mean square error, is little affected for mild-to-moderate violations of the assumptions. Thus, standard approaches, readily available in statistical software, will often suffice. The results are illustrated using data from the Heart and Estrogen/Progestin Replacement Study using models to predict future blood pressure values.