Regression Methods for Pairwise Comparison Data

Abstract

Multi-objective decision making often requires the comparison of qualitatively different entities. For example, a forest owner has to assess the aesthetic and recreation values of the forest in addition to the income from selling wood. Pairwise comparisons can be used to elicit relative preferences concerning such entities. Eigenvalue techniques introduced by Saaty (1977) are one way to analyse pairwise comparisons data. A weak point of the original methodology has been that it does not allow a statistical analysis of uncertainties in judgements. The eigenvalue technique also requires that all entities have been compared with each other. In many applications, this is impracticable because of the large number of pairs. The number of judges can also be large, and there can be missing observations. Moreover, it is frequently of interest to analyse how different attributes of the entities, or different attributes of the judges, influence the relative preference. In this paper, we first review our previous work with an alternative methodology based on regression analysis. Then, we show how explanatory variables can be incorporated. The construction of the design matrix is detailed and the interpretation of the results is discussed.