Application of 'delete = replace' to deletion diagnostics for variance component estimation in the linear mixed model

• Published in: Journal of the Royal Statistical Society. Series B, Statistical methodology Vol. 66; no. 1; pp. 131 - 143
• Main Authors: Haslett, John, Dillane, Dominic
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing 01.02.2004; Blackwell Publishers; Blackwell; Royal Statistical Society; Oxford University Press
• Series: Journal of the Royal Statistical Society Series B
• Subjects: Approximation; Conditional residuals; Estimation; Exact sciences and technology; General topics; Generalized least squares; Least squares; Leverage; Linear inference, regression; Linear models; Mathematical expressions; Mathematics; Matrix identities; Maximum likelihood estimation; Modeling; Modelling; Observational research; Probability and statistics; Restricted maximum likelihood; Sciences and techniques of general use; Statistical methods; Statistical variance; Statistics; Studies; Waste byproducts; Statistical method; Conditional distribution; Fitting; Variance estimation; Mixed model; Linear estimation; Maximum likelihood; Regression residual; Variance analysis; Variance component; Linear model; Variance
• ISSN: 1369-7412; 1467-9868
• DOI: 10.1046/j.1369-7412.2003.05211.x

'Delete = replace' is a powerful and intuitive modelling identity. This paper extends previous work by stating and proving the identity in more general terms and extending its application to deletion diagnostics for estimates of variance components obtained by restricted maximum likelihood estimation for the linear mixed model. We present a new, fast, transparent and approximate computational procedure, arising as a by-product of the fitting process. We illustrate the effect of the deletion of individual observations, of 'subjects' and of arbitrary subsets. Central to the identity and its application is the conditional residual.