[Rasch] scale shrinkage or expansion

matt.schulz at act.org matt.schulz at act.org
Tue Dec 13 03:09:50 EST 2005

Fellow Raschers:

I received the following inquiry recently:

   Are you aware of any research in which a linear transformation was used
   in the equating
   of Rasch item parameters?  While I realize that this practice is counter
   to the traditional
   Rasch approach, I wondered how one addressed differences in the
   variability of item difficulties
   from one administration to another.  Do you know of any testing programs
   that utilize a linear
   equating in a Rasch setting?  If so, do you know of any published
   studies addressing the impact
   of this non-traditional adjustment on the ability estimates?

I've had some experience with this, but not much.  One time, it seemed that
the effect of a low-vision rehabilitation program was to increase the
standard deviation of the item calibrations.  I suppose whenever this
happens, one looks for substantive explanations.  The items were skills
taught in the program and the question was "how hard is it for you to...."
(easy, moderate, hard).   Patients probably "understood" the skills
differently after experiencing the program.   As a result, they may have
been willing to give more extreme responses--"easy" and "hard"--to the
skills.  This would have spread out the items and/or pulled the threshold
calibrations in towards zero.

While such a thing could be explained with an attitude or rating scale
measure, I think it would be harder to explain with dichotomously-scored
items on an educational achievement test.  I would be concerned that it
wasn't a technical artifact of an increase in the variability of person

Any comments, experience, or literature to share?  Feel free to respond to
me directly.

Matthew Schulz
Department of Statistical Research
ACT, Inc.
Ph. 319-337-1468
matt.schulz at act.org

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