How to find an appropriate clustering for mixed-type variables with application to socio-economic stratification: written contribution to the discussion on the paper by Hennig and Liao

. Data with mixed-type (metricordinalnominal) variables are typical for social stratification, i.e. partitioning a population into social classes. Approaches to cluster such data are compared, namely a latent class mixture model assuming local independence and dissimilarity-based methods such as k-medoids. The design of an appropriate dissimilarity measure and the estimation of the number of clusters are discussed as well, comparing the Bayesian information criterion with dissimilarity-based criteria. The comparison is based on a philosophy of cluster analysis that connects the problem of a choice of a suitable clustering method closely to the application by considering direct interpretations of the implications of the methodology. The application of this philosophy to economic data from the 2007 US Survey of Consumer Finances demonstrates techniques and decisions required to obtain an interpretable clustering. The clustering is shown to be significantly more structured than a suitable null model. One result is that the data-based strata are not as strongly connected to occupation categories as is often assumed in the literature