float: Calculate floated variances

Description

Given a fitted model object, the float() function calculates floating variances (aka quasi-variances) for a given factor in the model.

Usage

float(object, factor, iter.max=50)

Arguments

object

a fitted model object

factor

character string giving the name of the factor of interest. If this is not given, the first factor in the model is used.

iter.max

Maximum number of iterations for EM algorithm

Value

An object of class floated. This is a list with the following components
coefvector of coefficients. These are the same as the treatment contrasts but the reference level is present with coefficient 0.
varvector of floating (or quasi-) variances
limitsBounds on the accuracy of standard errors over all possible contrasts

Details

float() implements the "floating absolute risk" proposal of Easton, Peto and Babiker(1992). This is an alternative way of presenting parameter estimates for factors in regression models, which avoids some of the difficulties of treatment contrasts. It was originally designed for epidemiological studies of relative risk (hence the name) but the idea is widely applicable.

A problem with treatment contrasts is that they are not orthogonal. The variances of the treatment contrasts may be inflated by a poor choice of reference level, and the correlations between them may be very high. float() associates each level of the factor, including the reference level, with a"floating" variance (or quasi-variance). Floating variances are not real variances, but they can be used to calculate the variance of any contrast by treating each level as independent. Plummer (2003) showed that floating variances can be derived from a covariance structure model applied to the variance-covariance matrix of the parameter estimates. This model can be fitted by minimizing the Kullback-Leibler information divergence between the true and distributions for the parameter estimates and the distribution given by the covariance structure model. Fitting is done using the EM algorithm.

In order to check the goodness-of-fit of the floating variance model, float() compares the standard errors predicted by the model with the standard errors derived from the true variance-covariance matrix of the parameter contrasts. The maximum and minimum ratios between true and model standard errors are calculated over all possible contrasts. These should be within 5 percent, or the use of the floating variances may lead to invalid confidence intervals.

References

Easton DF, Peto J and Babiker GAG (1991) Floating absolute risk: An alternative to relative risk in survival and case control analysis avoiding an arbitrary reference group. Statistics in Medicine, 10, 1025-1035.

Firth D and Mezezes RX (2004) Quasi-variances. Biometrika 91, 65-80.

Menezes RX(1999) More useful standard errors for group and factor effects in generalized linear models. D.Phil. Thesis, Department of Statistics, University of Oxford.