Abstract
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.
Highlights
The method of paired comparisons is a well established method for analysing preferences in many sciences
In this article we refer to a beta regression model that includes a linear predictor and a link function for both the location parameter μ and the precision parameter φ
The notation of a beta regression model as defined in (2) is suitable for modelling paired comparison data, where we want to model the mean of the response made on a bounded metric scale as a function of a set of covariates and parameters of the objects (λ) via a linear predictor
Summary
The method of paired comparisons is a well established method for analysing preferences in many sciences. We are not interested in scaling emotions but in directly modelling relative responses by comparing emotions to obtain an ordering of a set of J emotions on an interval scaled continuum where we could interpret the distances between the estimated parameters representing the emotions (i.e. the objects) of interest. The proposed metric paired comparison model allows the incorporation of subject covariates, where possible effects of the subject covariates on the ordering of the emotion parameters can be assessed This can be seen as an advantage of the paired comparison approach compared to the IRT models where item differences between subgroups are interpreted as model violations. Model selection can be done through a likelihood ratio test of nested models
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
