[Rasch] thresholds

Mike Linacre (RMT) rmt at rasch.org
Sat Jul 7 18:11:59 EST 2007


Dear Muy Ignoto:

Welcome to the Rasch list, and thank you for your questions.

To clarify, Rasch-Thurstone thresholds are always ordered, and are the 
intersections of the cumulative probabilities, for example: 0 vs 1+2+3 
points,  0+1 vs 2+3 points, 0+1+2 vs 3 points. Rasch-Andrich thresholds can 
be disordered, and are the intersections of the category probabilities, for 
example: 0 vs 1 point,  1 vs 2 points, 2 vs 3 points.

>Your question: Do we need to collapse the categories if the threshold are 
>disordered?
Reply: This depends on your purpose. For example, are you designing a new 
instrument or trying to make sense of an old dataset familiar to your 
audience? Also is the threshold disordering an accident of the current 
dataset or structural to the instrument? For instance, in survey 
instruments, Likert scales are sometimes printed as the response mechanism 
to true-false items. This confuses the respondents and such items are 
obvious candidates for collapsing categories.

Your objective is to produce Rasch measures that are useful and easy to 
communicate. The reason for linear measurement (which Rasch constructs) is 
to assist with clear thinking. So if collapsing categories makes the 
measures easier to understand, then do it. If collapsing categories makes 
the measures more obscure, then consider carefully the advantages and 
disadvantages.

Cordially,
Mike Linacre
rmt at rasch.org




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