[Rasch] Is the PCM a Rasch model?

Stephanou, Andrew Stephanou at acer.edu.au
Fri Mar 14 17:59:18 EST 2008


Robert,
 
I read the abstract of your paper for IOMW2008 and I am puzzled.  
http://home.att.net/~rsmith.arm/IOMW_prog.pdf <http://home.att.net/~rsmith.arm/IOMW_prog.pdf>  

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 viewed 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
 
Andrew Stephanou
ACER
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