Item Discrimination and Infit Mean-Squares

Descriptive approaches to item analysis parameterize differing central slopes in the empirical item characteristic curves (ICCs) as Item Discrimination, a. Rasch approaches detect differing slopes with quality-control fit statistics, most commonly the Infit mean-square (INFIT) statistic, an information-weighted chi-square statistic divided by its degrees of freedom. What is the numerical correspondence between INFIT and discrimination?

Item discrimination

Before such an investigation can have meaning, obvious malfunctions in the data such as guessing, carelessness, data entry errors and mis-scoring are screened out. Then, Figure below shows various idealized ICCs, plotted in the region of the latent variable on which the item is targeted. The box covers the region equivalent to p=.15 to p=.85 of the Rasch ogive, i.e., -1.7 to +1.7 logits. Discrimination a=1 is the Rasch ogive for a dichotomous item, and is shown extending beyond the box. Empirical ICCs outside the box are better diagnosed by the Outfit Mean-square statistics and point-biserial correlation.

Infit Mean-square vs. Discrimination

A simulation study produces the relationship shown in the Figure above. Central item discriminations from 0.5 to 1.7 produce good fit to the Rasch model, provided the part of the ICC away from the center is in reasonable conformance. This suggests that, for reasonably homogeneous items, empirical differences in item discrimination have no meaningful impact on measurement.

John Michael Linacre

Lawshe's (1948) Item discrimination nomograph

First, divide the sample into two strata (high and low). Second, compute the percentage of each strata succeeding on each item. Third, locate the two percentage points, one on each side of the nomograph. Fourth, the item discrimination is at the point where a line joining the two points crosses the middle line.
C.H. Lawshe, Jr. Principles of Personnel Testing. New York: McGraw-Hill, 1948, p. 190

Item Discrimination and Infit Mean-Squares. Linacre, J.M. … Rasch Measurement Transactions, 2000, 14:2 p.743

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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
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