A default conjugate prior for variance components in generalized linear mixed models (comment on article by Browne and Draper)

For a scalar random-effect variance, Browne and Draper (2005) have found that the uniform prior works well. It would be valuable to know more about the vector case, in which a second-stage prior on the random effects variance matrix D is needed. We suggest consideration of an inverse Wishart prior for D where the scale matrix is determined from the first-stage variance.