[Rasch] Fw: Disordered thresholds and collapsing

David Andrich david.andrich at uwa.edu.au
Mon Nov 5 20:32:29 EST 2012

In the case that the Rasch model fits for an ordered category item, then in theory, collapsing categories will create misfit.  This results because collapsing categories is only justified if the discrimination at the threshold between two categories is 0. It also implies that collapsing after data are collected is different from collapsing categories and collecting data in new categories.

If thresholds are reversed, and it looks as if there might be too many categories for the respondents and so on,  then it is in order to collapse categories to EXPLORE what kind of new system of categories, with a smaller number of categories, might work. In a particular data set it might be relevant to report both sets of results, and have more confidence in the collapsed ones. However, in principle, collapsing categories to this end cannot be the final solution to the problem. It cannot be because it would not be very defensible to collect data knowing in advance that there is a problem with the scoring. So the category system needs correcting.

 The above story holds if the data fit the Rasch model on most traditional criteria and if there are no other evident reasons why there might be reversed thresholds.

However, reversed thresholds can be a symptom of many things - for example multidimensionality within an item and poor alignment of persons and items, but not necessarily, and so on. For example, the Undecided (Neutral) etc category in the Strongly Disagree, Disagree, Neutral, Agree, Strongly Agree  system often shows up with reversed thresholds. The middle category is tapping into something that is not part of the continuum. Therefore, the substantive set up, the possible substantive reasons why the thresholds are disordered needs to be understood and experimented with rather than just collapsing categories as an end in itself.  An example is provided in 

Andrich, D., de Jong, J. H.A.L & Sheridan, B.E. (1997).Diagnostic opportunities with the Rasch model for ordered response categories. Chapter 4. In J. Rost and R. Langeheine (Eds.), Applications of Latent Trait and Latent Class Models in the Social Sciences. Waxmann Verlag GMBH:  Münster and New York, pp. 58-68.

Thus there is no necessarily simple solution to categories not working as intended. 

Other References (from which further references can be found of course).

Andersen, E.B. (1977). Sufficient statistics and latent trait models. Psychometrika, 42, 69-81.

Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43 (4), 561-574.

Andrich, D. (1979). A model for contingency tables having an ordered response classification. Biometrics, 35 (2), 403-415.

Andrich, D. (1995). Models for measurement, precision and the non-dichotomization of graded responses. Psychometrika,  60, (1) 7-26.

Andrich, D. (1995).  Further remarks on the non-dichotomization of graded responses. Psychometrika,   60  (1) 37-46.

Andrich, D. (2013) An expanded derivation of the threshold structure of the polytomous Rasch rating model which dispels any "threshold disorder controversy". Educational and Psychological Measurement.(In press, available on line).

Rasch, G. (1966). An individualistic approach to item analysis. In P.F. Lazarsfeld and N.W. Henry, (Eds.).  Readings in Mathematical Social Science (pp.89-108).  Chicago: Science Research Associates.

Hope this helps. 

David Andrich, BSc MEd W.Aust., PhD Chic, FASSA
Chapple Professor 
david.andrich at uwa.edu.au
Graduate School of Education
The University of Western Australia
M428, 35 Stirling Highway, 
Western Australia , 6009

Telephone: +61 8 6488 1085
Fax: +61 8 6488 1052
CRICOS Code: 00126G
Pearson Psychometric Laboratory

-----Original Message-----
From: rasch-bounces at acer.edu.au [mailto:rasch-bounces at acer.edu.au] On Behalf Of Thomas Salzberger
Sent: Monday, 5 November 2012 4:50 PM
To: Rasch at acer.edu.au
Subject: Re: [Rasch] Fw: Disordered thresholds and collapsing

Dear all,

Anthony asked me whether I could forward the message to the acer list, which I do hereby,


> ----- Forwarded Message -----
> From: Anthony James <luckyantonio2003 at yahoo.com>
> To: "rasch at acer.edu.au" <rasch at acer.edu.au>
> Sent: Sunday, November 4, 2012 3:45 PM
> Subject: Disordered thresholds and collapsing
> Dear all,
> I heard from some colleagues that collapsing categories in the case of 
> disordered thresholds is problematic and is not recommended. 
> Apparently this is a very recent development in rating scale analysis. 
> Can you please comments on this or refer me to some sources?
> Cheers
> Anthony

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