Fitting paired comparison models in R

Paired comparison models in loglinear form are generalised linear models and can be fitted using the IWLS algorithm. Unfortunately, the design matrices can become very large and thus a method is needed to reduce computational load (relating to both space and time). This paper discusses an algorithm for fitting loglinear paired comparison models in the presence of many nuisance parameters which is based on partition rules for symmetric matrices and takes advantage of the special structure of the design matrix in Poisson loglinear models. The algorithm is implemented as an R function. Some simple examples illustrate its use for fitting both paired comparison models and (multinomial) logit models. 1 Some definitions for loglinear paired comparison models The basic paired comparison model (or Bradley-Terry model) can be written in loglinear formu-lation as ln E(yjj′h) = θjj ′ + ah(λj − λj′) , (1) where yjj′h is the observed number of decisions for category h in the comparison between objects j and j′, and E(yjj′h) is the expected number. The λs describe the location of the objects o