Question: An item "Discrimination Index" is shown in Wright & Stone's book, Best Test
Design (1979, p. 52), but is not described in detail. What is it? Is it useful?
K. L., Hong Kong
Answer: This Discrimination Index was a feature of the Rasch computer program, BICAL. It is described in MESA Research Memorandum, 23B, by B.D. Wright, R.J. Mead, & S.R. Bell, June 1979. Here is what is written on pages 15 and 16:
If the data ... produced characteristic curves which varied in slope, then the person-item logit could be expressed as
In this form, γni is the difference between a "true" logit response and the Rasch model with which we have attempted to explain it. If the Rasch model adequately accounts for the data, the regression in Equation 22 should have a slope of zero.
In terms of estimates, this expression can be written as
[but yni can be approximated from the Rasch ICC as]
Therefore an indication of αi can be calculated as
[where y.i is the mean of the residuals for item i, and m.i is the mean of the person-item logits, bn-di.]
This is the residual index given in BICAL output.
Comment: Item discrimination is conceptualized as a property of the central slope of the item characteristic curve (ICC). This index, however, is strongly influenced by outliers (e.g., lucky guesses, careless mistakes). This drawback might be overcome by dropping or down-weighting off-target responses. On the other hand, Wright & Stone (p. 53) claim this index to be less affected by sample targeting and dispersion than the point-biserial correlation.
Discrimination, Guessing and Carelessness Asymptotes: Estimating IRT Parameters with Rasch.Linacre J.M. Rasch Measurement Transactions, 2004, 18:1 p.959-960
BICAL item discrimination index. Wright BD, Mead RJ, Bell SR. Rasch Measurement Transactions, 2002, 16:1 p.869
|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|
|Forum||Rasch Measurement Forum to discuss any Rasch-related topic|
Go to Top of Page
Go to index of all Rasch Measurement Transactions
AERA members: Join the Rasch Measurement SIG and receive the printed version of RMT
Some back issues of RMT are available as bound volumes
Subscribe to Journal of Applied Measurement
Go to Institute for Objective Measurement Home Page. The Rasch Measurement SIG (AERA) thanks the Institute for Objective Measurement for inviting the publication of Rasch Measurement Transactions on the Institute's website, www.rasch.org.
|Coming Rasch-related Events|
|June 26 - July 24, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com|
|June 29 - July 1, 2020, Mon.-Wed.||Measurement at the Crossroads 2020, Milan, Italy , https://convegni.unicatt.it/mac-home|
|July - November, 2020||On-line course: An Introduction to Rasch Measurement Theory and RUMM2030Plus (Andrich & Marais), http://www.education.uwa.edu.au/ppl/courses|
|July 1 - July 3, 2020, Wed.-Fri.||International Measurement Confederation (IMEKO) Joint Symposium, Warsaw, Poland, http://www.imeko-warsaw-2020.org/|
|Aug. 7 - Sept. 4, 2020, Fri.-Fri.||On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com|
|Oct. 9 - Nov. 6, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|June 25 - July 23, 2021, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com|
The URL of this page is www.rasch.org/rmt/rmt161n.htm