Correlated Errors in the Random Model

The usual one-way random model for the analysis of variance is broadened to allow for negative correlation between true residuals in the same row or cluster. This gives rise to an essential unidentifiability of parameters. Nonetheless, the likelihood function is typically such that the joint posterior distribution of all parameters is quite informative and there is enormous evidence for negative correlation whenever the sum of squares within is sufficiently large. Indeed, as this sum of squares goes to infinity, the joint posterior distribution converges to a limiting distribution which is very nearly the same as that in which it is known a priori that residuals are negatively correlated in the most extreme way possible.