Modal, transitional: RE: [Rasch] Interpretation of Item Plot

Stephen Humphry shumphry at cyllene.uwa.edu.au
Wed Mar 28 00:03:46 EST 2007


Hi Mike.

If the thresholds are disordered in your larva-pupa-adult cycle, then  
the point at which the organism is equally likely classified as a  
larva/pupa is higher on the developmental continuum than the point at  
which the organism is equally likely classified as pupa/adult. This is  
simply not the order of development. I am yet to see an explanation  
that deals with this basic, general problem (example in Andrich, 2005).

The brevity or otherwise of the phase does not alter this implication.  
Apart from anything else, the measurement scale is a developmental  
one, which may have a non-linear relationship with time. For example,  
time spent as an adult is relatively large but little development may  
occur.

You say: "a modal category has ordered Rasch-Andrich thresholds, a  
transitional category does not". I'm not really sure what you mean by  
this statement. Categories don't literally 'have' thresholds, of course.

On the algebra, severe misfit to the dichotomous model does not alter  
sufficiency. It does, however, mean that sufficiency is not much use  
in the empirical case.

Steve

Quoting "Mike Linacre (RMT)" <rmt at rasch.org>:

>
>> Andrew, Greg, et al.
>
> Andrew asked:
> Could you please explain what you mean by transitional and modal
> categories?  Does the Rasch model make such a distinction?
>>
> Reply:
> Transitional vs. modal is a substantive distinction in the practical
> use of the rating scale. In rating scales, modal categories correspond
> to longer-lasting or wider stages, likely to be observed by most
> observers of a developmental process. Transitional categories
> correspond to shorter-lasting or narrower stages which may be missed by
> most observers of a developmental process. For instance, in
> baby-development, most parents notice "immobile, crawling, walking".
> Crawling is a modal category. But in the mosquito life-cycle, larva -
> pupa - adult, it is easy to for the periodic observer to miss the pupa
> stage, which may only last a day or two. Pupa is a transitional
> category.
>
> In Rasch terms, a modal category has ordered Rasch-Andrich thresholds,
> a transitional category does not. But this distinction does not affect
> the algebra of the Rasch model, nor the crucial requirement that
> category counts be sufficient statistics for the parameter estimates.
>
> Hope this helps,
> Mike L.





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