Perceptual mapping using the basic structure matrix decomposition

Abstract

Perceptual mapping techniques are used to graphically represent perceptions of brands in a category, companies in an industry, and so forth. The data required to construct perceptual maps using typical methods can be difficult for respondents to provide and time-consuming to collect. An alternative, but relatively obscure perceptual mapping technique is rooted in correspondence analysis, and involves a fundamental matrix decomposition. Data requirements for this approach are simple. For example, a simple brand-attribute matrix, each cell containing the frequency of respondents stating that the respective attribute applies to the respective brand, could serve as the input data for the map. The data is treated as a contingency table, and the matrix whose elements are the deviations between observed and expected frequencies, adjusted for the respective expected frequencies, is decomposed to obtain the basic mapping coordinates. The resultant mapping approach is shown to be basically equivalent to correspondence analysis.