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 Publications
Rasch Measurement Transactions (free, online) Rasch Measurement research papers (free, online) Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Applying the Rasch Model 3rd. Ed., Bond & Fox Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr. Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
in Spanish: Análisis de Rasch para todos, Agustín Tristán Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez

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