Manual Estimation of "Partial Credit" Item Difficulties and Rasch-Andrich thresholds

Computer programs are routinely used to estimate Rasch measures. But is your program functioning correctly? Are the estimates based on the intended data? Are they based on the model you think you specified? A quick manual check of the computer's results can reassure you, or point you to a discrepancy.

Estimates for partial credit items, i.e., items specified to have unique rating scales, can be awkward to verify. Here is one approach. Imagine a sample of students who respond to both a dichotomous item and a polytomous "partial credit" items. We take the reported difficulty of the dichotomy, item i, as the benchmark difficulty. From this we estimate the difficulty of the dichotomy, Djk, between each pair of two adjacent categories, k-1 and k, of the partial credit item, j.

From their respective Rasch models,

So that

We can use this equivalence to estimate the difficulty of all the {Djk}. The mean item difficulty is

So that, within the item, the adjacent category dichotomies, Fjk, are located at

Here is an example from Items 12 and 14 of the "Liking for Science" data (Wright and Masters, 1982), specified as "partial credit".

Paired Frequencies
for "Liking for Science" items 12 and 14.
(Item 12 recoded 0,1)
N00N01N02N10N11N12
56292825

According to an analysis, the difficulty of the dichotomous item i=12, is -1.14. So that for item j=14,

In this example, the reported estimates are -.71 and 1.30, somewhat more central than the values, - 1.55 and 1.50, given by our approximation.

Andrew Stephanou, Australian Council for Educational Research

Manual estimation of partil credit item difficulties. Stephanou A. … 16:1 p.867


Manual estimation of partil credit item difficulties. Stephanou A. … Rasch Measurement Transactions, 2002, 16:1 p.867



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
Rasch Books and Publications: Winsteps and Facets
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 Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes Rasch Models for Solving Measurement Problems (Facets), George Engelhard, Jr. & Jue Wang 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
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

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