Various varying variances: The challenge of nuisance parameters to the practising biostatistician.

The 1997 Biometrics paper by Mike Kenward and James Roger has become a citation classic (more than 1260 citations by End June 2013 according to Google Scholar) and the solution that they proposed to deal with the problem of significance tests of fixed effects in REML models is now incorporated in many software packages and accepted by all biostatisticians as the method of choice. Nevertheless, it does not solve all problems, since there is more to analysis than just significance and since the problems that models with more than one variance pose arise in many contexts. In this paper, I discuss some problems and applications and make some tentative suggestions as to how they may be tackled. My excuse for raising problems I do not solve is that it may inspire James and Mike to complete what they started.