Perceptual Mapping

Attribute-based maps begin from consumer ratings of brands on named attributes and use factor analysis, principal components, or correspondence analysis to place brands and attribute vectors in a shared space, so the axes are tied to the attributes you measured. Similarity-based maps begin from direct judgments of how similar pairs of brands are and use multidimensional scaling to recover positions whose distances reproduce those similarities, without requiring any attribute list. Carroll and Green highlight that the similarity-based route can surface perceptual dimensions you never thought to measure, while the attribute-based route gives directly interpretable axes. The choice depends on whether you already know the relevant attributes and on whether you want interpretability or discovery.

Almost always two for communication, sometimes three, but the right number is a trade-off between fit and interpretability. In MDS you examine how the stress (the mismatch between map distances and input dissimilarities) falls as dimensions are added, looking for an elbow where extra dimensions buy little fit; in factor or correspondence analysis you look at variance or inertia explained. Carroll and Green caution that forcing everything into two dimensions when stress is high distorts the relationships, while using many dimensions defeats the visualization goal. A defensible map reports its fit statistic and justifies the chosen dimensionality rather than assuming two dimensions are adequate.

Not necessarily. Perceptual maps show how similar brands are perceived to be, which is a strong hint about substitutability but not direct evidence of it. Two brands can sit close on attributes yet draw different buyers, or sit apart yet compete because of price or availability. For decisions that hinge on actual substitution, perceptual maps should be validated against behavioral data — brand-switching matrices or cross-price elasticities from choice models such as Kamakura and Russell's latent-class approach. Used together, the perceptual map explains why brands are seen as alternatives and the choice model confirms whether buyers treat them as such, giving a fuller picture of competitive structure.