On Estimating Approximate Degrees of Freedom

Inference in linear models with multiple random effects is often complicated by variance estimators with distributions that are not exact multiples of chi-squared variates.Using a result attributed to Satterthwaite, one can approximate these estimators to a chi-square with appropriate degrees of freedom.These degrees of freedom, which can be used to find percentiles for tests of hypotheses and confidence intervals, are generally functions of the unknown variance components and hence must be estimated.This article investigates approximate degrees of freedom estimators and proposes a class of alternatives to the one in general use.