[Rasch] RMT Article

rsmith rsmith at jampress.org
Sat Sep 7 06:23:25 EST 2013

I read with interest the recent note in RMT V27, N2, by Royal and Raddatz that contained a cautionary tale about equating test forms for certification and licensure exams.  By the end of the note, I was troubled, by what I feel is a common misunderstanding about the properties of Rasch measurement.  

Their tale begins with a test administration and the investigation of item quality and functioning before attempting to equate the current form to a previously established standard.
It is widely known that the properties of item invariance that allow equating in the Rasch model hold, if and only if, the data fit the Rasch model.  The investigation of the fit of the data to the model should be investigated in the initial stage of equating.  The authors state, "Preliminary item analyses reveal the items appear to be sound and functioning."  One assumes that the fit of the data to the model was confirmed in this process, though it is not explicitly stated.  As the story continues, we find, in fact, that the equating solution does not hold across the various subgroups represented in the analysis and the calibration sample is subsequently altered to produce a different and more logical equating solution.  

This suggests that the estimates of item difficulty were not freed from the distributional properties of the sample.  Hence, the data can not fit a Rasch model.  One would hope that it is not necessary to get to the very end of the equating process before discovering that the estimates of item difficulty are not invariant and the link constant developed for equating is not acceptable.  

What then is the cause of the problem?  Without independent confirmation, I would suggest that the fit statistics used in the preliminary analysis lacked the power to detect violations of this type of first-time vs. repeater invariance.  This is easily corrected with the use of the between group item fit statistic available in Winsteps.  It will not solve the problem lack of fit to the Rasch model, but it will let you know there is a problem before you get too far into the equating process.  Developing an item bank that measures both types of examinees fairly is an entirely different issue, and one that should be addressed.  The lack of item invariance across subgroups is a classic definition of item bias.

Richard M. Smith, Editor
Journal of Applied Measurement
P.O. Box 1283
Maple Grove, MN  55311, USA
website:  www.jampress.org
phone: 763-268-2282
fax: 763-268-2782 

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