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Biometrika 2004 91(1):65-80; doi:10.1093/biomet/91.1.65
© 2004 by Biometrika Trust
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Quasi-variances

David Firth1 and Renée X.De Menezes2

1 Department of Statistics, University of Warwick, Coventry CV4 7AL, U.Kdf{at}stats.warwick.ac.uk 2 Department of Medical Statistics, Leiden University Medical Centre, Postbus 9604, 2300 RC Leiden, Netherlands r.x.menezes{at}lumc.nl

In statistical models of dependence, the effect of a categorical variable is typically described by contrasts among parameters. For reporting such effects, quasi-variances provide an economical and intuitive method which permits approximate inference on any contrast by subsequent readers.Applications include generalised linear models, generalised additive models and hazard models. The present paper exposes the generality of quasi-variances, emphasises the need to control relative errors of approximation, gives simple methods for obtaining quasi-variances and bounds on the approximation error involved, and explores the domain of accuracy of the method. Conditions are identified under which the quasi-variance approximation is exact, and numerical work indicates high accuracy in a variety of settings.

Key Words: Bradley-Terry model; Comparison intervals; Floating absolute risk; Generalised linear model; meta analysis; Proportional hazards

Received September 2002. Revised July 2003


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