# [Rasch] Why are Rasch measures linear?

Stone, Gregory gstone at UTNet.UToledo.Edu
Tue Sep 4 04:21:32 EST 2007

```Michael and David are by far more advanced scholars than I, but I would like to go back to Ronald Fisher who took ordinal scale data and transformed it into interval scale data through simple logarithmic transformations.  Of course it had none of the other properties that the Rasch transformation includes beyond the notion of linearity, however the transformation to linearity was performed statistically many, many years before Rasch, at least from a mathematical perspective.  Linearity itself seems to me to be the simplest of the Rasch transformations, rather than the most complex.  Independence and the construction of variables are far more difficult to explain generally.  If I am mistaken about Fisher, I hope someone will correct me!

Gregory

Gregory E. Stone, Ph.D., M.A.

Assistant Professor of Research and Measurement
The Judith Herb College of Education
The University of Toledo, Mailstop #914
Toledo, OH 43606   419-530-7224

Editorial Board, Journal of Applied Measurement     www.jampress.org

Board of Directors, American Board for Certification of Teacher Excellence     www.abcte.org

For information about the Research and Measurement Programs at The University of Toledo and careers in psychometrics, statistics and evaluation, email gregory.stone at utoledo.edu.

-----Original Message-----
From: rasch-bounces at acer.edu.au on behalf of Anthony James
Sent: Sun 9/2/2007 8:41 AM
To: rasch at acer.edu.au
Subject: [Rasch] Why are Rasch measures linear?

Dear all,
I have a basic question on the Rasch model.
We always hear that Rasch measures are linear while raw scores aren't. Linearity is defined as "equal increments to the difficulty or ability measures when one more unit is added to a person's or an item's location".
What I can't grasp is why Rasch measures are linear? What's magic about the Rasch measures. Once I heard  "Rasch measures are cnstructed to be linear". But how?
I'd be grateful if someone explains in laymen terms that why Rasch measures are linear.
Regards
Anthony

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