Robust two-stage estimation in hierarchical nonlinear models

Hierarchical models encompass two sources of variation, namely within and a mong individuals in the population; thus, it is important to identify outli ers that may arise at each sampling level. A two-stage approach to analyzin g nonlinear repeated measurements naturally allows parametric modeling of t he respective variance structure for the intraindividual random errors and interindividual random effects. We propose a robust two-stage procedure bas ed on Huber's (1981, Robust Statistics) theory of M-estimation to accommoda te separately aberrant responses within an experimental unit and subjects d eviating from the study population when the usual assumptions of normality are violated. A toxicology study of chronic ozone exposure in rats illustra tes the impact of outliers on the population inference and hence the advant age of adopting the robust methodology. The robust weights generated by the two-stage M-estimation process also serve as diagnostics for gauging the r elative influence of outliers at each level of the hierarchical model. A pr actical appeal of our proposal is the computational simplicity since the es timation algorithm may be implemented using standard statistical software w ith a nonlinear least squares routine and iterative capability.