[Rasch] Interpretation of Item Plot

Mike Linacre (RMT) rmt at rasch.org
Mon Mar 26 18:55:29 EST 2007

Stephen, Greg, et al.

As you say, Stephen, there is certainly an inferential problem if the 
categories in Greg's rating scale are all intended to be modal. And the 
Rasch model does require that Greg's categories are ordered qualitatively.

But your statement "The structure of the Rasch model requires they [the 
Rasch-Andrich thresholds] are ordered." appears to be too strong.  The 
integer-scoring of ordered categories is independent of the Rasch-Andrich 
thresholds - e.g., www.rasch.org/rmt/rmt131a.htm . A mathematical feature 
of derivations of the Rasch Rating Scale model is that the pair-wise 
log-odds of adjacent categories is unconstrained by the value of the 
log-odds of any other adjacent pair of categories. Your 
statement  introduces a constraint on the overall pattern of 
adjacent-category log-odds similar to that in the (non-Rasch) Graded 
Response model. If you can provide a reference to a mathematical proof of 
this requirement, I would be delighted to publish it in RMT. I did not 
notice it in Wright & Master's "Rating Scale Analysis", nor in Gerhard 
Fischer's "The Derivation of the Polytomous Rasch Model"  (Chap. 16, "Rasch 
Models: ...", Fischer & Molenaar), nor in Erling Andersen's  "Rating Scale 
Model" (Handbook of Modern Item Response Theory).

May I suggest this wording? "The structure of the Rasch model is 
inferentially more secure when they [the Rasch-Andrich thresholds] are 

Mike Linacre,
Editor, Rasch Measurement Transactions

At 3/26/2007, Stephen Humphry wrote:
>Whether the thresholds are ordered as intended is an empirical question. 
>The structure of the Rasch model requires they are ordered. Ordered 
>thresholds are the basis for the definition of integer scoring of ordered 
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