This article suggests a new approach for modelling longitudinal paired comparison data. As individual preferences may change from one time point to another, we propose extending the basic log-linear Bradley-Terry (BT) model by incorporating a Markovian structure with temporal withincomparison dependence parameters and parameters indicating the amount of change of the unknown preference parameters of the objects. We illustrate this approach by analysing a student survey relating to statistics course design with three time points. Keywords Bradley-Terry model • log-linear model • longitudinal paired comparison data • Markov chain • temporal change of preference parameters

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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This article proposes an alternative method of making comparative judgements in multivariate paired comparisons (PCs) where judgements about change are made directly by comparing an object at two time points for each of a series of attributes. The application deals with the design of shop window displays where products should be arranged by teams of vocational students according to aesthetic principles (attributes). The photos of the students’ window displays at time 1 (before feedback) and at time 2 (after feedback) were compared by judging each attribute as to whether it was fulfilled better at time 1 or at time 2. An advantage of this PC approach over an alternative of a scoring system is the possibility to assess even subtle changes of various aspects of attractiveness, which cannot easily be measured using a score. To analyse these data, we used earlier work which developed both a multivariate PC pattern model for multi-attribute data and a PC model over time and defined a multivariate PC model of changes (MPCC). The model can be fitted as a non-standard Poisson log-linear model and provides estimates of change for the three attributes for time 2 and we were able to check for possible interaction effects between these attributes.

Die Analyse von Präferenzdaten gewinnt im Bereich der Sozial- und Wirtschaftswissenschaften, insbesondere im Marketing, und der Psychologie immer mehr an Bedeutung. Das Buch bietet einen Streifzug durch die wichtigsten Paarvergleichsmodelle sowie deren Umsetzung mit Hilfe der frei verfügbaren Statistiksoftware R und dem Paket prefmod. Besondere statistische, mathematische oder softwaretechnische Kenntnisse werden dabei nicht vorausgesetzt.