[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
ordered."
Cordially,
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
>categories,
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