Quotation Grand, Alexandra, Dittrich, Regina. 2015. Modelling assumed metric paired comparison data: Application to learning related emotions. Austrian Journal of Statistics 44 (1): S. 3-15.




In this article we suggest a beta regression model that accounts for the degree of preference in paired comparisons measured on a bounded metric paired comparison scale. The beta distribution for bounded continuous random variables assumes values in the open unit interval (0, 1). However, in practice we will observe paired comparison responses that lie within a fixed or arbitrary fixed interval [-a, a] with known value of a. We therefore transform the observed responses into the interval (0, 1) and assume that these transformed responses are each a realization of a random variable which follows a beta distribution. We propose a simple paired comparison regression model for beta distributed variables which allows us to model the mean of the transformed response using a linear predictor and a logit link function where the linear predictor is defined by the parameters of the logit-linear Bradley Terry model. For illustration we applied the presented model to a data set obtained from a student survey of learning related emotions in mathematics.


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Publication's profile

Status of publication Published
Affiliation WU
Type of publication Journal article
Journal Austrian Journal of Statistics
Language English
Title Modelling assumed metric paired comparison data: Application to learning related emotions.
Volume 44
Number 1
Year 2015
Page from 3
Page to 15
Reviewed? Y
URL http://www.ajs.or.at/index.php/ajs/article/view/vol44-1-1
DOI http://dx.doi.org/10.17713/ajs.v44i1.25


The analysis of rank order preference data based on Bradley-Terry type models
Dittrich, Regina (Former researcher)
Grand, Alexandra (Wirtschaftsuniversität Wien, Austria)
Institute for Statistics and Mathematics IN (Details)
Competence Center for Empirical Research Methods WE (Details)
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