[Rasch] Is the PCM a Rasch model?

rsmith.arm at att.net rsmith.arm at att.net
Sat Mar 15 01:46:10 EST 2008

If you would like to know the answer to this question, there is a session at IOMW with Robert Massof, David Andrich, William Fisher, and Ronald Mead that will deal exclusively with these issues.  It would be very informative to join us at IOMW 2008 in New York next weekend.

IOMW 2008 will offer over 50 presentations in 14 sessions during the two day meeting.  There are several computer software sessions available, as well as the usual paper and symposium sessions.  The preliminary program is available and it promises to be a interesting IOMW.  Registration is $40 USD (early) and $50 USD (late).  To receive the reduced early registration fee your payment information must be received by today (March 14, 2008).  

Please Note:

With the high security in New York City, it will be necessary to present a photo ID to enter the NYU classroom buildings.  Each participant's name must appear on the attendee list provided to security.  If you are planning to use on-site registration, it will be necessary to e-mail the organizing committee  by March 17 to have your name added to the attendee list.  E-mail addresses for this purpose are listed below.  IOMW will meet in rooms 713 and 714 of the Silver Center, 100 Washington Square East, New York, NY  10003.

The registration from is available on the Journal of Applied Measurement web site (http://www.jampress.org).  Click on IOMW 2008  on the right side and scroll down to the registration form.  The form is available as a printable pdf that can be mailed, or e-mailed when completed.  The same information is also available on the Data Recognition Corporation web site (http://www.datarecognitioncorp.com).  
Richard M. Smith, Editor 
Journal of Applied Measurement 

P.O. Box 1283 
Maple Grove, MN 55311 USA 
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voice: 763-268-2282 (w) 
fax: 763-268-2782 

-------------- Original message from "Stephanou, Andrew" <Stephanou at acer.edu.au>: -------------- 


I read the abstract of your paper for IOMW2008 and I am puzzled.  
Is the Partial Credit Model a Rasch Model? 
Presenting Author: Robert W. Massof, Johns Hopkins University 
Abstract: Rasch models must satisfy the requirement of statistical sufficiency of person and item raw scores and separability of model parameters. The Andrich rating scale model (RSM) satisfies these requirements, but because of the interaction between items and response category thresholds, the Masters partial credit model (PCM) does not. When attempting to prove statistical sufficiency of the item raw score and separability of parameters, Masters implicitly made assumptions that allowed the item-dependent step measures to be factored out, thereby making the item-dependent step raw score vector appear to be a sufficient statistic for the step measures. However, his arguments in effect require the trivial condition that there is only a single item. The relationship between person measures and the expected response is free to vary across items, therefore, Master's implicit assumptions are not valid and the item raw score is not a sufficient statistic. However, the PCM can be v
as a scale equating device, thereby preserving scale invariance post hoc.

David Andrich and Mike Linacre have shown that there are no two different models, the Rating Scale and the Partial Credit, but one: the polytomous Rasch model.

How is it possible for one version of the Rasch polytomous model to satisfy the requirements of statistical sufficiency of person and item raw scores and separability of model parameters but not for the other?

I would appreciate if you send me your paper.  Thanks.


Andrew Stephanou
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