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- Publisher
- Cambridge University Press
- Copyright
- 1980 The Psychometric Society
- ISSN
- 0033-3123
- eISSN
- 1860-0980
- DOI
- 10.1007/bf02294077
- Publisher site
- See Article on Publisher Site
Abstract
Abstract We present a new algorithm, MAPCLUS (MAthematicalProgrammingCLUStering), for fitting the Shepard-Arabie ADCLUS (forADditiveCLUStering) model. MAPCLUS utilizes an alternating least squares method combined with a mathematical programming optimization procedure based on a penalty function approach, to impose discrete (0,1) constraints on parameters defining cluster membership. This procedure is supplemented by several other numerical techniques (notably a heuristically based combinatorial optimization procedure) to provide an efficient general-purpose computer implemented algorithm for obtaining ADCLUS representations. MAPCLUS is illustrated with an application to one of the examples given by Shepard and Arabie using the older ADCLUS procedure. The MAPCLUS solution uses half as many clusters to achieve nearly the same level of goodness-of-fit. Finally, we consider an extension of the present approach to fitting a three-way generalization of the ADCLUS model, called INDCLUS (INdividualDifferencesCLUStering).
Journal
Psychometrika – Cambridge University Press
Published: Jun 1, 1980
Keywords: Psychometrics; Assessment, Testing and Evaluation; Statistics for Social Sciences, Humanities, Law; Statistical Theory and Methods