Modelling Class Uncertainty in the Geodemographic Output Area Classification

Geodemographics is the study of people by where they live, and historically has relied in part on census information to provide essential variables. In 2005 the Office for National Statistics for England and Wales published a geodemographic classification of output areas (OAs; the smallest published areas of enumeration for the UK) of the 2001 UK Census. Uniquely among UK examples of such classifications not only are the classes to which each OA is assigned published for free with no restriction on use, but the difference between each OA and all class centroids are also made available. In this paper these differences (being Euclidian distances in the classification feature space) are used to introduce uncertainty by softening the classification using the methods derived from fuzzy c-means and the possibilistic c-means classifications. The former applies a probabilistic assumption that all fuzzy memberships for a particular OA sum to unity while the latter does not. This assumption (which is the same as that behind the published OA classification) may generate results which are potentially misleading because the fuzzy c-means method forces OAs into classes to which they may have relatively little similarity while minimising the importance of classes to which they may have a larger affinity. If the fuzzy memberships or possibilities were to be integrated with other socioeconomic variables which are also conceived as fuzzy sets for geodemographic applications (decision making for government resource allocation, site location modelling or marketing, for example), then the two results would produce different outcomes. It is suggested that the possibilistic c-means are the more useful although they do lead to the possibly confusing but analytically rich situation where one OA may have minimal affinity with any class, at the same time as others may have strong affinity with many classes.