A comparison of plots for monothetic clustering, with applications to microbial communities and educational test development

Monothetic clustering for multivariate binary data provides a method of identifying variables whose levels identify the different patterns of responses. The default graphical summary of the standard version of this method provides information on the variables used to split the observations into groups and the proportions of the responses in the groups but not the levels of the responses in each cluster. A modified graph is proposed to provide fuller interpretations of the clustering results. The methods are applied to two examples and contrasted with other approaches to clustering multivariate binary responses. One application involves the clustering different bacterial clones presence/absence throughout distinct strata (or sections) in ice cores from Pony Lake, Antarctica, where the interest is in the full patterns of responses in the different clusters. The second is from a test developed to measure elementary education mathematics coaches knowledge of different aspects of mathematics coaching. In this second application, the interest lies more with questions that define distinct groups of individuals than with the entire pattern of responses