An alternative outlier model for outliers in linear mixed effects models
by
Beverley Gogel
Queensland Department of Primary Industries
Coauthors: Sue Welham (IACR-Rothamsted), Brian Cullis (NSW Agriculture), Ari Verbyla (BiometricsSA, The University of Adelaide and South Australian Research and Development Institute)

Outliers are data observations that fall outside the range of the response data and/or design space. They are common in experimental research data for reasons such as transcription error or technical equipment malfunction. Often outliers are quickly identified and addressed, that is, corrected, removed from the data or retained for subsequent analysis. However, in many cases they are completely anomalous and the most appropriate approach for treating them is unclear. Of greater concern is that influential outliers, that is, data observations that have an unusually large influence on the fitted model, can be left undetected and ultimately result in poorly selected models, poor inference, and inappropriate decisions based on these inferences.

Case deletion diagnostics are commonly used to detect outliers in normal theory fixed effects models and this approach has been extended by Christensen, Pearson and Johnson (1992) for mixed linear models. An alternative is to detect data observations with inflated variance. In this paper we extend the alternative outlier model (AOM) for outlier detection in fixed linear models (Thompson, 1985) to accommodate mixed linear models. We first consider the AOM for individual observations with inflated variance. We then consider an AOM for the other random effects in the model. We will demonstrate the techniques with examples.

Christensen, R., Pearson, L. M. and Johnson, W. (1992). Case deletion diagnostics for mixed models, Technometrics 34: 38-45.

Thompson, R. (1985). A note on restricted maximum likelihood estimation with an alternative outlier model, Journal of the Royal Statistical Society Series B 47: 53-55.

Date received: September 6, 2002