Abstract
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.
Dedicated to our friend and esteemed colleague Ewa Orłowska, with gratitude for a long lasting and fruitful cooperation
The ordering of authors is alphabetical and equal authorship is implied.
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We should like to express our gratitude to the anonymous referees for careful reading and useful suggestions.
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Düntsch, I., Gediga, G. (2018). Guttman Algebras and a Model Checking Procedure for Guttman Scales. In: Golińska-Pilarek, J., Zawidzki, M. (eds) Ewa Orłowska on Relational Methods in Logic and Computer Science. Outstanding Contributions to Logic, vol 17. Springer, Cham. https://doi.org/10.1007/978-3-319-97879-6_14
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