Research on new computational approaches to complex random effects models

Statistical modelling of Correlated Data thruogh Pseudo-Likelihood [Firth, Feddag, Turner] (Statistical inference, statistical computation).

This project is exploring various aspects of approximate likelihood approaches to inference in models of dependence which involve complex structures of random effects. Complex random effects arise in connection with longitudinal data of various types, including data on competition, on networks of relationships, on multi-item test perfomance, on legislative voting, and many other modern social-research contexts. The essence of the "random" effects, in all cases, is to capture variation that is not predicted perfectly by available explanatory variables. This is crucial for reliable conclusions; neglecting important sources of variation typically results in non-negligible bias and/or substantial over-statement of the precision of estimates made from data.

The technical difficulties created by complex systems of random effects are of two main kinds: computational complexity arising from the need to calculate high-dimensional integrals repeatedly and with reasonable accuracy; and potential sensitivity of conclusions to secondary modelling assumptions, that is to say assumptions which are not crucial to the framing of research questions but which are needed in order to specify a full likelihood function for the purposes of statistical analysis. The focus of this project is on some recently suggested <em>approximate</em> likelihood methods which aim to overcome one or both of these types of difficulty; the class of "composite likelihood" methods, based on low-order marginal or conditional views of the full dataset, is particularly promising among these. The aims are to investigatethe statistical properties of such methods in some "leading case" contexts of interest in social research, and to implement the methods in user-friendly, fully documented, open-source software in order that they become routinely available to the wider research community.

Early progress has, of necessity, been mostly on the technical aspects, and in the application areas of generalized Bradley-Terry models for pairwise comparison and of Rasch-type models for longitudinal item response.

Some of the models studied are inherently non-linear in character, and this has led naturally to implementation of some of the methods as extensions to the "gnm" (generalized nonlinear models) software package, whose authors are members of the project team and for which the prestigious John M Chambers Statistical Software Award was made in 2007 by the American Statistical Association.

The project has established an extensive network of communication with relevant experts internationally, especially in the area of composite likelihoods. Based on those valuable contacts a major international research workshop is being organised at Warwick in April 2008.  For more information on this please visit:  http://go.warwick.ac.uk/complik2008