Item Discrimination and Rasch-Andrich Thresholds

Rasch dichotomous items are modeled to have the same (or known) discrimination. The inter-adjacent-category discrimination of polytomous Rasch items is also modeled to be the same (or known), but the overall discrimination of polytomous items depends on the distance between its Rasch-Andrich thresholds and so can vary across items and instruments..

Consider a five category rating scale, modeled by a set of 4 equally spaced Rasch-Andrich thresholds. Then the overall item discrimination can vary from very steep to almost flat depending on the distance between the threshold values.

The plot shows the relationship between uniform threshold spacing, x, and the item-discrimination slope, a, of an equivalent logistic ogive with the range y = 0-4 score points given by

A discrimination of a ≥ 1.0 implies that the polytomy is equivalent to summing 4 independent dichotomous 0-1 items. When a = 1.0 the items are of equal difficulty. When the inter-threshold distance is negative, the Rasch-Andrich threshold are "disordered".

It can be seen that one advantage of using Rasch polytomies over independent dichotomous items is that a polytomy can provide higher item discrimination while maintaining the desirable measurement properties of a Rasch model. This is useful for items targeting pass-fail decisions and computer-adaptive testing. This is also one situation in which disordered thresholds can be advantageous.

John Michael Linacre

Item Discrimination and Rasch-Andrich Thresholds, Linacre J.M. Linacre J.M. … Rasch Measurement Transactions, 2006, 20:1 p. 1054

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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