Assessing the assumption of symmetric proximity measures in the context of multidimensional scaling

Applications of multidimensional scaling often make the assumption of symmetry for the population matrix of proximity measures. Although the likelihood of such an assumption holding true varies from one area of research to another, formal assessment of such an assumption has received little attention. The present article develops a nonparametric procedure that can be used in a confirmatory fashion or in an exploratory fashion in order to probabilistically assess the assumption of population symmetry for proximity measures in a multidimensional scaling context. The proposed procedure makes use of the bootstrap technique and alleviates the assumptions of parametric statistical procedures. Computer code for R and S-Plus is included in an appendix in order to carry out the proposed procedures.