Estimating Item Discriminations with Rasch Models

Plots of empirical item characteristic curves (ICCs) enable one to estimate the empirical item discrimination, at least as well as a 2-PL IRT computer program. This is because 2-PL discrimination estimation is degraded by the imputation of a person distribution and by arbitrary constraints placed on discrimination values. It is also skewed by accidental outliers which the eye can disregard.

Figure 1. Empirical and model ICCs.

On a plot such as Figure 1 draw in the line that, to your eye, matches the central slope of the empirical item characteristic curve (ICC). In Figure 1, the dots indicate the Rasch-model-predicted ICC. The points marked `x' indicate the empirical values, obtained by averaging the observed responses, `0' and `1', for persons whose measures are estimated to be in the .1 logit interval centered on the `x'. When a dot and an `x' coincide, a `*' is shown. The line follows the trail of `x' and `*'.

Estimate the logit (x-axis) distance from where the line intercepts the .0 score value to where it intercepts the 1.0 score value (for dichotomies). The logit distance here is about 4.0 logits.

Use the nomogram in Figure 2 to estimate empirical item discrimination. In this nomogram, looking at the middle traceline, a logit distance of 4.0 logits, corresponds to a logit discrimination of 1.0, in accordance with model prediction. Shorter distances, i.e., steeper slopes, correspond to higher discriminations.

Figure 2. Nomogram for item discrimination.

In Figure 2, there are 3 lines in order to simplify comparison and reporting of results in an IRT context. 2-PL programs generally report their results in probits. So the probit discrimination for logits distances is given by the upper line. That corresponding to a 4-logit distance is 1.7. On the other hand, if one is looking at plot scaled in probits, instead of logits, one would look at the lower line to find the logit discrimination.

John M. Linacre

Estimating item discriminations with Rasch models. Linacre JM. … 16:1 p.868

Estimating item discriminations. Linacre JM. … Rasch Measurement Transactions, 2002, 16:1 p.868

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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