[Rasch] Why are Rasch measures linear?

commons commons at tiac.net
Tue Sep 4 09:15:49 EST 2007

Dear Gregory:  


This is not possible.  Consider the follow series


The underlying distances are actually 


1    14   15    16    22    23

These have the ordinals associated with the underlying distances of 

1    2      3     4       5       6


Taking the log of the ordinals does nothing to linearize this series.





From: rasch-bounces at acer.edu.au [mailto:rasch-bounces at acer.edu.au] On Behalf
Of Stone, Gregory
Sent: Monday, September 03, 2007 2:22 PM
To: Anthony James; rasch at acer.edu.au
Subject: RE: [Rasch] Why are Rasch measures linear?


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 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

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.


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