Similarity measures for response patterns on dichotomously scored items

Response patterns from test, questionnaires, or other kind of evaluation instruments can give important information about latent variables which cannot be directly observed, such as the "ability" of the respondent individuals. The study of similarity between response patterns leads to a classification of the respondents that can explain the latent variable under a new perspective. There are several known similarity measures, mostly developed in fields such as the bibliometric and scientometric research, which are based on co-occurrences between "objects", and satisfy certain properties which unfortunately don’t suit to our problem. Taking inspiration from these measures, we propose a class of similarity measures for response patterns on dichotomously scored items. This study is meant as an example of applying these measures within the item response theory framework, and as a critical assessment of the usefulness of this approach. Our method focuses on the position of respondents in the multidimensional space spanned by the aggregated subject-subject co-occurrences. A number of choices/parameters can be left to the user, but we provide default options reflecting our preferences.