infonet-economy

Mixed linear models are used to analyse data in many settings. These models have in most cases a multivariate normal formulation. The maximum likelihood estimator (MLE) or the residual MLE (REML) are usually chosen to estimate the parameters. However, the latter are based on the strong assumption of exact multivariate normality. Welsh and Richardson (1997) have shown that these estimators are not robust to small deviations from the multivariate normality. This means in practice for example that a small proportion of data (even only one) can drive the value of the estimates on their own. Since the model is multivariate, we propose in this paper a high breakdown robust estimator for very general mixed linear models, that inlcude for example covariates. This robust estimator belongs to the class of S-estimators (Rousseeuw and Yohai 1984) from which we can derive the asymptotic properties for the inference. We also use it as a diagnostic tool to detect outlying subjects. We discuss the advantages of this estimator compared to other robust estimators proposed previously and illustrate its performance with simulation studies and the analysis of four datasets.