Generalized Nonlinear Models: Theory, Computation and Extensions

This project will develop a systematic approach to a large class of statistical models, which unifies and extends many methods that have been developed for particular applications across a wide range of scientific disciplines. The class of generalized nonlinear models includes as prominent sub-classes some of the cornerstones of statistical methodology, notably generalized linear models and parametric nonlinear regression. The current project will develop unified methods for approximate inference and for computation in such models. In addition, innovative methods for summary and display of the results of an analysis, including graphical methods, will be extended to this broader class of models, as will methods for the systematic treatment of variation that is not explicitly predicted within the model (so-called random effects ). Particular attention will be paid to instances that are of direct relevance to current practical work, notably models which include multiplicative terms; these have been important recently in research fields as diverse as experimental psychology, crop science and sociology, for example. A key thread running through all of the work will be the novel use of over-parameterized representations of statistical models, designed to allow imaginative modelling strategies to be constructed naturally and pursued without the need to pay undue attention to technical details (typically connected with parameter identifiability) at each step. The results of the research will appear in the peer-reviewed scientific literature and in fully documented open-source software, thus making these methodological developments immediately available to practitioners.