Multidimensional Unfolding and the use of alternative input scales

Abstract

Non-metric Multidimensional Unfolding (MDU) techniques have been misused for some time due to some degeneracy problems. Recently, the PREFSCAL algorithm has been proposed which deals properly with degenerate solutions. However, and in spite of the interest of MDU outputs – perceptual maps depicting two groups of entities and illustrating their proximities – there are still some open issues regarding MDU applications. In particular, one may ask whether different input scales can have significant impact on MDU solutions. Although this subject has been approached in Multidimensional Scaling (MDS) quite a long time ago, it seems that it is now pertinent to address it in the context of MDU. The main goal of the present study is to analyse the association between MDU input, concerning the use of alternative scales, and MDU performance. Simulated data with uniform distribution are randomly generated, different scales with different numbers of response categories are considered and MDU analysis is performed using PREFSCAL. The results are evaluated based on the proportion of variance on disparities accounted for by the corresponding distances. Inferential results indicate that there are significant differences in MDU model adjustment originated by the use of alternative input scales. An application referred to the use of alternative communication technologies is presented which illustrates the association between the use of different MDU input scales and MDU performance. The obtained results agree with the ones p22rovided by the simulation study. Furthermore, they add some insights concerning the relationship between Portuguese individuals and alternative communication channels.