Perceptual mapping using ordered logit analysis

This study is to present a new method for constructing a perceptual map based on logit analysis. This is an extension of the explosion logit model of an individual choice to a problem of perceptual mapping giving rise to advantages over existing methods in various aspects. Firstly, input data format is flexible and user-friendly. Unlike traditional methods which typically requires a total dissimilarity ordering on all the pairs of the objects, it allows a partial ordering to any rank depth and a ‘pivot’ ordering which gives a dissimilarity ordering of objects with respect to a specific ‘pivot’ or ‘anchored’ object. Secondly, it introduces the concept of an evoked set into perceptual mapping and allows a respondent to make judgments only within his/her evoked set. This, together with the first point, contributes to the reduction of the respondents’ burden and the data noise. Thirdly, Monte Carlo experiments have revealed that our ML estimates give a considerably better fit to data than ALSCAL, one of the most widely used algorithms of MDS. Particularly worth noting is that our method using the data ranked only up to the top two thirds gives as good a fit as ALSCAL using totally ordered data. Although not exploited here, opening up a way for statistical inference in nonmetric MDS would be yet another advantage. An empirical application is made to a Canadian car market for illustration.