Rasch-Andrich Thresholds and Rasch-Thurstone Thresholds

The Rasch-Andrich thresholds (step parameters) in the Partial Credit (or Rating Scale) Model are not "thresholds" in the sense that the rest of the world (beginning with Urban in the 1800s and including Thurstone) understands that term.

The polytomous Rasch model for multiple categories is built out of successive applications of Rasch's dichotomous model, applied conditionally to successive pairs of adjacent categories. Thus the magnitudes of the conditionally-defined step parameters can take any order, and their interpretation is also conditional on the consideration of categories two at a time. To mark out a variable for meaningful interpretation, these conditionally-defined parameters must be brought together, yielding the probabilities of responses in particular categories. This produces the set of unconditionally-defined Rasch-Thurstone category thresholds.

For those of us who build variables for a living, Rasch-Thurstone thresholds are indeed the useful way to understand partial credits and rating scales. Ray Adams' book on Science Learning shows just how practical and convincing building variables with Rasch-Thurstone thresholds can be!

Science learning in Victorian schools, 1990, Raymond J. Adams, Brian A. Doig, Malcolm J. Rosier. ACER: Australian Council for Educational Research

Rasch-Andrich Thresholds and Rasch-Thurstone Thresholds. Masters GN. … Rasch Measurement Transactions, 1992, 5:4 p.191

Rasch Books and Publications
Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, 2nd Edn. George Engelhard, Jr. & Jue Wang	Applying the Rasch Model (Winsteps, Facets) 4th Ed., Bond, Yan, Heene	Advances in Rasch Analyses in the Human Sciences (Winsteps, Facets) 1st Ed., Boone, Staver	Advances in Applications of Rasch Measurement in Science Education, X. Liu & W. J. Boone	Rasch Analysis in the Human Sciences (Winsteps) Boone, Staver, Yale
Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes	Statistical Analyses for Language Testers (Facets), Rita Green	Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments (Facets), George Engelhard, Jr. & Stefanie Wind	Aplicação do Modelo de Rasch (Português), de Bond, Trevor G., Fox, Christine M	Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
Exploring Rating Scale Functioning for Survey Research (R, Facets), Stefanie Wind	Rasch Measurement: Applications, Khine	Winsteps Tutorials - free Facets Tutorials - free	Many-Facet Rasch Measurement (Facets) - free, J.M. Linacre	Fairness, Justice and Language Assessment (Winsteps, Facets), McNamara, Knoch, Fan
Other Rasch-Related Resources: Rasch Measurement YouTube Channel
Rasch Measurement Transactions & Rasch Measurement research papers - free	An Introduction to the Rasch Model with Examples in R (eRm, etc.), Debelak, Strobl, Zeigenfuse	Rasch Measurement Theory Analysis in R, Wind, Hua	Applying the Rasch Model in Social Sciences Using R, Lamprianou	El modelo métrico de Rasch: Fundamentación, implementación e interpretación de la medida en ciencias sociales (Spanish Edition), Manuel González-Montesinos M.
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar	Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch	Rasch Models for Measurement, David Andrich	Constructing Measures, Mark Wilson	Best Test Design - free, Wright & Stone Rating Scale Analysis - free, Wright & Masters
Virtual Standard Setting: Setting Cut Scores, Charalambos Kollias	Diseño de Mejores Pruebas - free, Spanish Best Test Design	A Course in Rasch Measurement Theory, Andrich, Marais	Rasch Models in Health, Christensen, Kreiner, Mesba	Multivariate and Mixture Distribution Rasch Models, von Davier, Carstensen

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