float() function calculates
floating variances (a.k.a. quasi-variances) for a given factor in the model.float(object, factor, iter.max=50)floated. This is a list with the following
componentsfloat() function 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, but
the idea is widely applicable. Treatment contrasts are not orthogonal. Consequently, the variances of
treatment contrast estimates may be inflated by a poor choice of
reference level, and the correlations between them may also be high.
The float() function associates each level of the factor with a
"floating" variance (or quasi-variance), including the reference
level. Floating variances are not real variances, but they can be
used to calculate the variance error of 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 contrast estimates. This model can be fitted by minimizing the
Kullback-Leibler information divergence between the true distribution
of the parameter estimates and the simplified 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,
the float() function 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-based 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.
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.
Plummer M (2003) Improved estimates of floating absolute risk, Statistics in Medicine, 23, 93-104.
ftrend, qvcalc