[Rasch] The Rasch Rating Model and the Disordered Threshold Controversy

Rense Lange rense.lange at gmail.com
Sat Jul 7 19:13:18 EST 2012

Yes, it is controversial as this goes precisely to the heart of some non-Rasch rating scale models where higher raw scores can mean lower trait levels than do lower raw scores and vice-versa. 

Rense Lange

On Jul 7, 2012, at 10:36 AM, Jeremy Hobart wrote:

> Hi
> Is it really controversial that a higher "score" on a rating scale ought to mean more of the problem being measured than a lower score? If so 4cm is actually shorter than 3cm.
> Please can you circulate the full reference as well as the naked abstract, (I didnt get the full ref). Can the authors please make the PDF available so that we can make a judgement?
> Also, I'm sure David Andrich has some comments to make. It would be be good to see those.
> Jeremy
> On 6 Jul 2012, at 21:58, "SR Millis" <srmillis at yahoo.com<mailto:srmillis at yahoo.com>> wrote:
> The Rasch Rating Model and the Disordered Threshold Controversy
> 1.  Raymond J. Adams<http://intl-epm.sagepub.com/search?author1=Raymond+J.+Adams&sortspec=date&submit=Submit> adams at acer.edu.au<mailto:adams at acer.edu.au>
> 2.  Margaret L. Wu<http://intl-epm.sagepub.com/search?author1=Margaret+L.+Wu&sortspec=date&submit=Submit>
> 3.  Mark Wilson<http://intl-epm.sagepub.com/search?author1=Mark+Wilson&sortspec=date&submit=Submit>
> Abstract
> The Rasch rating (or partial credit) model is a widely applied item response model that is used to model ordinal observed variables that are assumed to collectively reflect a common latent variable. In the application of the model there is considerable controversy surrounding the assessment of fit. This controversy is most notable when the set of parameters that are associated with the categories of an item have estimates that are not ordered in value in the same order as the categories. Some consider this disordering to be inconsistent with the intended order of the response categories in a variable and often term it reversed deltas. This article examines a variety of derivations of the model to illuminate the controversy. The examination of the derivations shows that the so-called parameter disorder and order of the response categories are separate phenomena. When the data fit the Rasch rating model the response categories are ordered regardless of the (order of the) values of the parameter estimates. In summary, reversed deltas are not necessarily evidence of a problem. In fact the reversed deltas phenomenon is indicative of specific patterns in the relative numbers of respondents in each category. When there are preferences about such relative numbers in categories, the patterns of deltas may be a useful diagnostic.
> ~~~~~~~~~~~
> Scott R Millis, PhD, ABPP, CStat, PStat®
> Board Certified in Clinical Neuropsychology, Clinical Psychology, & Rehabilitation Psychology
> Professor
> Wayne State University School of Medicine
> Email: aa3379 at wayne.edu<mailto:aa3379 at wayne.edu>
> Email: srmillis at yahoo.com<mailto:srmillis at yahoo.com>
> Tel: 313-993-8085
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