Multilevel Modelling

a three-day introductory workshop to multilevel modelling using MLwiN will take place If you plan to run any workshops using MLwiN, please notify Amy Burch and she will advertise these workshops on the multilevel web site. In the standard multilevel model lower level units are uniquely classified within one higher level unit, for example students within schools or people within households. In many kinds of data, however, individuals will 'belong' to more than one such unit. Thus, in a longitudinal study students may move between schools so that the school 'effect' must be considered as shared among the schools attended. Likewise, over time, individuals may experience more than one household. In order to model such data multiple membership models have been developed. The talk will describe such models, introducing a new notation and examples of applications. An application to the analysis of poultry salmonella outbreaks will be presented. The lowest level unit is a poultry flock whose members are derived from several parent flocks and there is also a cross classification of the parent flocks with the poultry farms. The modelling approach provides estimates of the contributions of each parent flock to the infection probability. The methodology can also be used for fitting spatial models. An interesting application arises in education and other areas where measurements are available for individuals, for example achievement scores, and also for groups of individuals where there is a single group response. Under suitable conditions, the joint analysis of individual and group responses allows the estimation of the effective contribution each individual makes towards the group response together with the relationship between that and the individual's separate response. General-purpose Bayesian software packages, for example WinBUGS, that utilize MCMC methods are now being used widely by quantitative researchers. To make such software as flexible as possible, MCMC methods that can be adapted to fit the widest range of statistical models have been preferred. Originally, Gibbs sampling algorithms primarily through the AR sampler were used to fit models using univariate updates with the restriction that all conditional posteriors be log concave. More recently this restriction has been removed by using adaptive (random-walk) Metropolis samplers for parameters without log concave distributions. These samplers are used (where necessary) in both the WinBUGS and MLwiN software packages. In this talk, we discuss another feature of certain statistical models-'constrained' variance matrices-which cannot currently be dealt with in general purpose packages. By …