A Bayes Linear Analysis of Multilevel Models

In this thesis, Bayes Linear methods for modeling multilevel data are presented and discussed. Second-order exchangeability judgements are exploited to formulate subjectivist versions of multilevel models. Bayes linear methods are applied to estimate model parameters and for diagnostic checks. Closed-form expressions of estimators are derived, allowing insight into relationships between the quantities thereof. The canonical analysis and resolution transforms are used to guide sample design and sample size determination under cost constraints. A finite version of a multilevel model is formulated, analysed and compared to infinite versions, giving further insight into sample design issues via the finite resolution transform. A new Bayes Linear Minimum Variance Estimation (BLIMVE) approach is de- veloped to estimate variances. Estimated variances are used to perform two-stage Bayes linear analysis of more complex multilevel models. The methods developed are shown to be applicable in cases of small level-2 samples. The Bayes linear analy- ses of multilevel models are applied to an educational data set using special-purpose codes written in the R Statistical Language.