Robust Two-Stage Estimation in Hierarchical Nonlinear Models
Article first published online: 24 MAY 2004
Volume 57, Issue 1, pages 266–272, March 2001
How to Cite
Yeap, B. Y. and Davidian, M. (2001), Robust Two-Stage Estimation in Hierarchical Nonlinear Models. Biometrics, 57: 266–272. doi: 10.1111/j.0006-341X.2001.00266.x
- Issue published online: 24 MAY 2004
- Article first published online: 24 MAY 2004
- Received September 1998. Revised June 2000. Accepted July 2000.
- Mixed effects;
- Repeated measurements
Summary. Hierarchical models encompass two sources of variation, namely within and among individuals in the population; thus, it is important to identify outliers that may arise at each sampling level. A two-stage approach to analyzing nonlinear repeated measurements naturally allows parametric modeling of the respective variance structure for the intraindividual random errors and interindividual random effects. We propose a robust two-stage procedure based on Huber's (1981, Robust Statistics) theory of M-estimation to accommodate separately aberrant responses within an experimental unit and subjects deviating from the study population when the usual assumptions of normality are violated. A toxicology study of chronic ozone exposure in rats illustrates the impact of outliers on the population inference and hence the advantage of adopting the robust methodology. The robust weights generated by the two-stage M-estimation process also serve as diagnostics for gauging the relative influence of outliers at each level of the hierarchical model. A practical appeal of our proposal is the computational simplicity since the estimation algorithm may be implemented using standard statistical software with a nonlinear least squares routine and iterative capability.