Generalized Nonlinear Models: Theory, Computation and Extensions

Lead Research Organisation: University of Warwick
Department Name: Statistics


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.


10 25 50
publication icon
Cattelan M (2013) Dynamic Bradley-Terry modelling of sports tournaments Dynamic Modelling of Sports Tournaments in Journal of the Royal Statistical Society: Series C (Applied Statistics)

publication icon
Firth D (2011) On improved estimation for importance sampling in Brazilian Journal of Probability and Statistics

publication icon
Firth D (2005) Bradley-Terry Models in R in Journal of Statistical Software

publication icon
GrĂ¼n B (2012) Extended Beta Regression in R : Shaken, Stirred, Mixed, and Partitioned in Journal of Statistical Software

publication icon
Kosmidis I (2010) A generic algorithm for reducing bias in parametric estimation in Electronic Journal of Statistics

publication icon
Kuha J (2011) On the index of dissimilarity for lack of fit in loglinear and log-multiplicative models in Computational Statistics & Data Analysis

Description This research was methodological development in statistics and statistical computation. We developed a wide range of novel, enabling methods for applied researchers to use, and disseminated them through papers, conferences and (especially) published, open-source software.
Exploitation Route Primarily through the use of our open-source, fully documented software packages in the R ecosystem. The packages resulting from this funded project are: "gnm"; "BradleyTerry2", "betareg" and "vcdExtra", all available from the Comprehensive R Archive Network ( This software is designed to enable other researchers to use appropriate tools for high-level statistical analysis of substantial data.

The authoritative software-tracking system, Depsy, rates all four of the above-mentioned software packages at or above the 85th percentile in terms of usage and impact, among the >8000 published R packages currently available (as at February 2017). This means that all four of these software outputs are now in very wide use. See for the details of the Depsy ratings.
Sectors Aerospace, Defence and Marine,Agriculture, Food and Drink,Chemicals,Communities and Social Services/Policy,Construction,Digital/Communication/Information Technologies (including Software),Education,Electronics,Energy,Environment,Financial Services, and Management Consultancy,Healthcare,Leisure Activities, including Sports, Recreation and Tourism,Government, Democracy and Justice,Manufacturing, including Industrial Biotechology,Pharmaceuticals and Medical Biotechnology,Retail,Security and Diplom

Description The main findings of the project have all been implemented and published in open-source software, which we continue to maintain. Researchers worldwide are using the software -- they ask us interesting questions about further development, and they frequently express their appreciation!
First Year Of Impact 2010
Sector Agriculture, Food and Drink,Education,Environment,Healthcare,Pharmaceuticals and Medical Biotechnology,Other