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KEELE UNIVERSITY CENTRE FOR MEDICAL STATISTICS SEMINAR SERIES on BIOSTATISTICS 2003/2004 NO 1: Wednesday, May 5th 2004, at 12:00 pm What are 'the' residuals for the linear model? Professor John Haslett Trinity College, Dublin We consider taxonomy of residuals for the linear model Y = X ? + ? where ? ~ N (0,V). This model includes classical multiple regression with correlated errors, but it also covers models for multivariate, spatial and/or time series data as well as random coefficient and 'mixed' models. Indeed its solution is very closely related to that of the much wider class of models that can be addressed through Generalised Estimating Equations. Despite the rather fundamental nature of the question and the maturity of the literature, and in contrast to the situation where V is diagonal, there is no single answer. Nevertheless the question is almost never addressed in the literature. There is typically an implicit assumption that the author and the reader instinctively share the same definition. In time series the underlying innovations provide the usual basis. In classical regression the 'distance from the line', being also based on the underlying random errors, is normal. In spatial work the cross-validation residual seems to be the standard. Are these the basically the same? Do issues arise in regression with auto-correlated errors, or in multi-level models, or where there is more than one source of random variation or where the where the random variation is multivariate? We propose a taxonomy and draw attention to three quite distinct types of residual: the marginal residual, the conditional residual and the innovation residual. We discuss the differences and the interrelationships. The conditional residual in particular is much under-appreciated despite being the natural starting point for deletion diagnostics in particular. Venue: Room 115 Computer Science, Third Floor, MacKay Building, Keele University - All welcome!! http://www.keele.ac.uk/cwis.html http://www.esci.keele.ac.uk/kudis/_campusguide/downloads/Keele_campus_guide_colour.pdf <http://www.keele.ac.uk/university/campus/cgm.pdf> **************************************** Janet Drewery Centre for Medical Statistics Mathematics Department MacKay Building Keele University Keele, Staffs ST5 5BG Tel: (01782) 583269 Fax: (01782) 584268 E-mail: [log in to unmask] ***************************************