Modelling the Effect of Subject-Specific Covariates in Paired Comparison Studies with an Application to University Rankings

Abstract

Preference decisions will usually depend on the characteristics of both the judges and the objects being judged. In the analysis of paired comparison data concerning European universities and students' characteristics, it is demonstrated how to incorporate subject-speci®c information into Bradley±Terry-type models. Using this information it is shown that preferences for universities and therefore university rankings are dramatically different for different groups of students. A log-linear representation of a generalized Bradley±Terry model is speci®ed which allows simultaneous modelling of subject-and object-speci®c covariates and interactions between them. A further advantage of this approach is that standard software for ®tting log-linear models, such as GLIM, can be used.

Subject-specific Bradley–Terry–Luce models with implicit variable selection

“…The adjacent categories BTL model can also be represented as a log-linear model, which has been extensively discussed in the literature (see Agresti, 1992;Dittrich et al, 1998;Dittrich et al, 2004;Dittrich et al, 2007). When the response consists of K = 2 categories, the binary BTL model (1) is a special case of the cumulative BTL model (4) and the adjacent categories BTL model (7).…”

“…Therefore, the ranking of the objects is the same for all subjects. However, in most applications it is to be expected that the preference for an object and thus the ranking of all objects depends on characteristics of the subject that makes the preference decision (Dittrich et al, 1998;Francis et al, 2002). To explicitly model this heterogeneity, we introduce subject-specific covariates x i,1 , .…”

“…To illustrate that our variable selection method works, we use the Community of European management schools (CEMS) data from Dittrich et al (1998), which was collected in a survey of 303 students of the Vienna University of Economics. The aim of the study was to investigate the preferences of students for studying at least one semester abroad in one of 6 different universities (London, Paris, Barcelona, St.Gallen, Milan and Stockholm) and to establish an overall ranking of these universities.…”

Extended ordered paired comparison models with application to football data from German Bundesliga

“…Explanatory variables of the latter type are more interesting when items are compared and preference is to be modeled as a function of characteristics of the person that chooses. Explanatory variables of this type have been considered, for example, by Dittrich et al (1998) when modeling the preference for European universities.…”

Modelling Assumed Metric Paired Comparison Data - Application to Learning Related Emotions

“…Several authors (e.g. Rao and Kupper 1967;Kousgaard 1976;Dittrich, Hatzinger, and Katzenbeisser 1998) have extended the BT model to incorporate a third category (ties) for indifference, i.e. no preference.…”