Linear Mixed Models with Flexible Distributions of Random Effects for Longitudinal Data
Article first published online: 21 MAY 2004
Volume 57, Issue 3, pages 795–802, September 2001
How to Cite
Zhang, D. and Davidian, M. (2001), Linear Mixed Models with Flexible Distributions of Random Effects for Longitudinal Data. Biometrics, 57: 795–802. doi: 10.1111/j.0006-341X.2001.00795.x
- Issue published online: 21 MAY 2004
- Article first published online: 21 MAY 2004
- Received February 2001. Revised March 2001. Accepted March 2001.
- Longitudinal data;
- Random effects;
- Seminonparametric density;
- Semipara-metric mixed effects model;
Summary. Normality of random effects is a routine assumption for the linear mixed model, but it may be unrealistic, obscuring important features of among-individual variation. We relax this assumption by approximating the random effects density by the seminonparameteric (SNP) representation of Gallant and Nychka (1987, Econometrics55, 363–390), which includes normality as a special case and provides flexibility in capturing a broad range of nonnormal behavior, controlled by a user-chosen tuning parameter. An advantage is that the marginal likelihood may be expressed in closed form, so inference may be carried out using standard optimization techniques. We demonstrate that standard information criteria may be used to choose the tuning parameter and detect departures from normality, and we illustrate the approach via simulation and using longitudinal data from the Framingham study.