Volume 62, Issue 3 p. 663-682

The metric-frequency measure of similarity for ill-structured data sets, with an application to family therapy

Célia M. D. Sales

Célia M. D. Sales

Department of Psychology and Sociology, Universidade Autónoma de Lisboa, Rua de Santa Marta, Lisboa, Portugal

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Peter P. Wakker

Corresponding Author

Peter P. Wakker

Economics Department, Erasmus University, Rotterdam, The Netherlands

Correspondence should be addressed to Professor Peter P. Wakker, Econometric Institute, Erasmus University, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands (e-mail: [email protected]).Search for more papers by this author
First published: 11 January 2011
Citations: 5


Similarity measures have been studied extensively in many domains, but usually with well-structured data sets. In many psychological applications, however, such data sets are not available. It often cannot even be predicted how many items will be observed, or what exactly they will entail. This paper introduces a similarity measure, called the metric-frequency (MF) measure, that can be applied to such data sets. If it is not known beforehand how many items will be observed, then the number of items actually observed in itself carries information. A typical feature of the MF is that it incorporates such information. The primary purpose of our measure is that it should be pragmatic, widely applicable, and tractable, even if data are complex. The MF generalizes Tversky's set-theoretic measure of similarity to cases where items may be present or absent and at the same time can be numerical as with Shepard's metric measure, but need not be so. As an illustration, we apply the MF to family therapy where it cannot be predicted what issues the clients will raise in therapy sessions. The MF is flexible enough to be applicable to idiographic data.