Bayesian Inference for Variance Components Using Only Error Contrasts

Patterson & Thompson (1971) proposed estimating the variance components of a mixed analysis of variance model by maximizing the likelihood of a set of error contrasts. In the present paper, a convenient representation is obtained for that likelihood. It is shown that, from a Bayesian viewpoint, using only error contrasts to make inferences on variance components is equivalent to ignoring any prior information on the fixed effects and using all the data.