Guttman Algebras and a Model Checking Procedure for Guttman Scales

  • Ivo DüntschEmail author
  • Günther Gediga
Part of the Outstanding Contributions to Logic book series (OCTR, volume 17)


We consider Guttman scales both from an algebraic and a statistical point of view. We present a duality between a class of algebras and Guttman scalable response structures, and show that the index of reproducibility is not always a reliable indicator for the Guttman scalability of a data set. Furthermore, we present a model checking procedure, and close with an example.


Item-response structure Guttman scales Concept lattice Discrete duality Model checking 



We should like to express our gratitude to the anonymous referees for careful reading and useful suggestions.


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Brock UniversitySt. CatherinesCanada
  2. 2.Institut für Evaluation und MarktanalysenJeggenGermany

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