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
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