ABSTRACT
In Chapters 2 and 4 the multivariate approach to repeated measures and longitudinal data was described in which no prior constraints were imposed on the covariance matrix Σ. Linear models for μ were formulated and fitted, and Σ was estimated without prejudice, i.e. without prior judgements such as constraint relationships between its elements. Now, while it is a good thing to be flexible and robust, not making assumptions about Σ which might be untrue, it can also be costly. Thus, with ten repeated measures there are 55 independent parameters in Σ to be estimated. (A p × p matrix, constrained only to be symmetric, as p(p +)/2 independent elements.) With a limited amount of data, this might leave too little information available for the aspects of main interest, i.e. usually those concerning μ. In Chapters 3 and 5 some structure was assumed for Σ which was meant to reflect the situation under which the observations were generated. As always, a balance has to be struck: with too little structure too many parameters might be left to estimate, leading to weaker inferences; with too much structure there is a risk of model misspecification, leading to apparently stronger, but biased, inferences.
