BICAL Item Discrimination Index

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

(21)

or

(22)

where

In this form, γ_ni 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

(23)

[but y_ni can be approximated from the Rasch ICC as]

Therefore an indication of α_i 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, b_n-d_i.]

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.

1. The Item Discrimination Index: Does it Work? Tristan Lopez A. … Rasch Measurement Transactions, 1998, 12:1 p. 626
2. BICAL item discrimination index. Wright BD, Mead RJ, Bell SR. … Rasch Measurement Transactions, 2002, 16:1 p.869
3. Item Discrimination Indices. Kelley T., Ebel R., Linacre, JM. … Rasch Measurement Transactions, 2002, 16:3 p.883-4

4. 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 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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