Quasi-variances in Xlisp-Stat and on the web

David Firth

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The most common summary of a fitted statistical model, a list of parameter estimates and standard errors, does not give the precision of estimated combinations of the parameters, such as differences or ratios. For this, covariances also are needed; but space constraints typically mean that the full covariance matrix cannot routinely be reported. In the important case of parameters associated with the discrete levels of an experimental factor or with a categorical classifying variable, the identifiable parameter combinations are linear contrasts. The QV Calculator computes "quasi-variances" which may be used as an alternative summary of the precision of the estimated parameters. The summary based on quasi-variances is simple and permits good approximation of the standard error of any desired contrast. The idea of such a summary has been suggested by Ridout (1989) and, under the name "floating absolute risk", by Easton, Peto & Babiker (1991). It applies to a wide variety of statistical models, including linear and nonlinear regressions, generalized-linear and GEE models, Cox proportional-hazard models for survival data, generalized additive models, etc.

The QV Calculator is written in Xlisp-Stat (Tierney, 1990) and can be used either directly by users who have access to Xlisp-Stat or through a web interface by those who do not. The user either supplies the covariance matrix for the effect parameters of interest, or, if using Xlisp-Stat directly, can generate that matrix by interaction with a model object.

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