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. (authors' abstract)

As Internet communities such as question-answer (Q&A) forums and online social networks (OSNs) grow in prominence as knowledge sources, traditional editorial filters are unable to scale to their size and pace. This absence hinders the exchange of knowledge online, by creating an understandable lack of trust in information. This mistrust can be partially overcome by a forum by consistently providing reliable information, thus establishing itself as a reliable source. This work investigates how algorithmic approaches can contribute to building such a community of voluntary experts willing to contribute authoritative information. This work identifies two approaches: a) reducing the cost of participation for experts via matching user queries to experts (question recommendation), and b) identifying authoritative contributors for incentivization (authority estimation). The question recommendation problem is addressed by extending existing approaches via a new generative model that augments textual data with expert preference information among different questions. Another contribution to this domain is the introduction of a set of formalized metrics to include the expert's experience besides the questioner's. This is essential for expert retention in a voluntary community, and has not been addressed by previous work. The authority estimation problem is addressed by observing that the global graph structure of user interactions, results from two factors: a user's performance in local one-to-one interactions, and their activity levels. By positing an intrinsic authority 'strength' for each user node in the graph that governs the outcome of individual interactions via the Bradley-Terry model for pairwise comparison, this research establishes a relationship between intrinsic user authority, and global measures of influence. This approach overcomes many drawbacks of current measures of node importance in OSNs by naturally correcting for user activity levels, and providing an explanation for the frequent disconnect between real world reputation and online influence. Also, while existing research has been restricted to node ranking on a single OSN graph, this work demonstrates that co-ranking across multiple endorsement graphs drawn from the same OSN is a highly effective approach for aggregating complementary graph information. A new scalable co-ranking framework is introduced for this task. The resulting algorithms are evaluated on data from various online communities, and empirically shown to outperform existing approaches by a large margin. / text

The purpose of this paper is to give a log-linear representation of a generalized Bradley-Terry (BT-) Model for paired comparisons which allows the incorporation of ties, order effects, concomitant variables for the objects and categorical subject specific covariates and interactions between all of them. An advantage of this approach is that standard software for fitting log-linear models, such as GLIM, can be used. The approach is exemplified by analysing data from an experiment concerning the ranking of European universities. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

This paper provides an alternative methodology for the analysis of a set of Likert responses measured on a common attitudinal scale when the primary focus of interest is on the relative importance of items in the set. The method makes fewer assumptions about the distribution of the responses than the more usual approaches such as comparisons of means, MANOVA or ordinal data methods. The approach transforms the Likert responses into paired comparison responses between the items. The complete multivariate pattern of responses thus produced can be analysed by an appropriately reformulated paired comparison model. The dependency structure between item responses can also be modelled flexibly. The advantage of this approach is that sets of Likert responses can be analysed simultaneously within the Generalized Linear Model framework, providing standard likelihood based inference for model selection. This method is applied to a recent international survey on the importance of environmental problems. (author's abstract) / Series: Research Report Series / Department of Statistics and Mathematics

This paper develops a new approach to the analysis of longitudinal paired comparison data, where comparisons of the same objects by the same judges are made on more than one occasion. As an alternative to other recent approaches to such data, which are based on Kalman filter- ing, our approach treats the problem as one of multivariate multinomial data, allowing dependence terms between comparisons over time to be incorporated. The resulting model can be fitted as a Poisson log-linear model and has parallels with the quadratic binary exponential distribution of Cox. An example from the British Household Panel Survey illustrates the approach. (author´s abstract) / Series: Research Report Series / Department of Statistics and Mathematics