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Discovery Algorithms for Hierarchical Relations

Published online by Cambridge University Press:  01 January 2025

Lewis C. Price ,
C. Mitchell Dayton  and
George B. Macready
Lewis C. Price*
Affiliation:
Macro Systems, Inc.
C. Mitchell Dayton
Affiliation:
University of Maryland
George B. Macready
Affiliation:
University of Maryland
*
Requests for reprints should be sent to Lewis C. Price, Macro Systems, Inc., 8630 Fenton Street, Suite 300, Silver Spring, Maryland 20910.
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Abstract

Two algorithms based on a latent class model are presented for discovering hierarchical relations that exist among a set of K dichotomous items. The two algorithms, stepwise forward selection and backward elimination, incorporate statistical criteria for selecting (or deleting) 0-1 response pattern vectors to form the subset of the total possible 2k vectors that uniquely describe the hierarchy. The performances of the algorithms are compared, using computer-constructed data, with those of three competing deterministic approaches based on ordering theory and the calculation of Phi/Phi-max coefficients. The discovery algorithms are also demonstrated on real data sets investigated in the literature.

Keywords

probabilistic modellatent class modelhierarchical relationslatent structure analysisdiscovery algorithms
Type
Original Paper
Information
Psychometrika , Volume 45 , Issue 4 , December 1980 , pp. 449 - 465
Copyright
Copyright © 1980 The Psychometric Society

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References

Reference Notes

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