Using Generalised Linear Models to Model Compositional Response by Dr Fiona Sammut (Friday 7 December at 12:00 in Lab 602, MP Building
A multivariate logit model which models the influence of explanatory variables on continuous compositional response variables is presented. This multivariate logit model generalises an elegant method that was suggested previously by Wedderburn (1974) for the analysis of leaf blotch data in the special case of two components, leading to naming this new approach as the generalised Wedderburn method. In contrast to the logratio modeling approach devised by Aitchison (1982, J. Roy Stat. Soc. B.), the multivariate logit model used under the generalized Wedderburn approach models the expectation of a compositional response variable directly and is also able to handle zeros in the data. The estimation of the parameters in the new model is carried out using the technique of generalized estimating equations (GEE). Desirable properties of the GEE estimator will be discussed. The theoretical results will be substantiated by simulation experiments, and properties of the new model are also studied empirically on some classic datasets from the literature.
