Advances in covariance modelling

Conventionally, in longitudinal studies, the mean structure has been thought to be more important than the covariance structure between the repeated measures on the same individual. Often, it has been argued that, with re- spect to the mean, the covariance was merely a `nuisance parameter' and, consequently, was not of `scientific interest'. Today, however, one can see that from a formal statistical standpoint, the inferential problem is entirely symmetric in both parameters. In recent years there has been a steady stream of new results and we pause to review some key advances in the expanding field of covariance modelling, In particular, developments since the seminal work by Pourahmadi (1999, 2000) are traced. While the main focus is on longitudinal data with continuous responses, emerging approaches to joint mean-covariance modelling in the GEE, and GLMM arenas are also considered briefly.