[Rasch] Help with equating partial credit items in pre - post test

Michael Lamport Commons commons at tiac.net
Wed Jun 18 02:14:51 EST 2008


We have been experimenting with equating in a somewhat novel way.  We 
know the or hierarchical of the items.  We do a Rasch analysis.  We find 
the average Rasch Scale score for the items of the same order of 
hierarchical complexity.  We use that to find the stage score.

Michael Lamport Commons

Stephen Humphry wrote:
> Mike. Good to see the 1999 NASA orbiter example I used in my 
> presentation at the January Rasch conference had an impact! That's 
> right. Equating of units has been loosely referred to on occasion by 
> various people for a long time. Because equating units of 
> scales implies a discrimination parameter, it's important to avoid 
> falling into the trap of the 2PL model in which sufficiency of Rasch 
> mdoels is destroyed if one wishes to adhere to Rasch's criterion on 
> invariance. This is possible under appropriate conditions, as I've 
> shown in terms of Rasch's (1977) concept of the frame of reference in 
> various presentations and papers, including the presentation in 
> January. Various factors, including person characteristics and 
> assessment conditions, may affect the discrimination in one frame of 
> reference relative to another, and therefore their units. 
> Discrimination is itself measurable, and therefore comparisons between 
> discrimination should be invariant also. This is the key: if 
> discrimination could not be measured, it would have no place in a 
> measurement model.
>  
> Regards,
>  
> Steve
>  
> Dr Stephen Humphry
> Graduate School of Education
> University of Western Australia
> 35 Stirling Highway
> CRAWLEY  WA  6009
> Mailbox M428
> P: (08) 6488 7008
> F: (08) 6488 1052
>
> ------------------------------------------------------------------------
> *From:* rasch-bounces at acer.edu.au [mailto:rasch-bounces at acer.edu.au] 
> *On Behalf Of *Mike Linacre (RMT)
> *Sent:* Monday, 2 June 2008 2:36 PM
> *To:* rasch at acer.edu.au
> *Subject:* [Rasch] Help with equating partial credit items in pre - 
> post test
>
> Thank you for your message, Steve.
>
> /You wrote: Mike. If there is a different unit, in principle the 
> responses in frames of reference that have different units (due to 
> different levels of discrimination) need to be modelled separately 
> first then brought onto a common scale.
>
> /Reply: Agreed! If the NASA experts organizing the Mars Climate 
> Orbiter had realized they had a "different unit" problem (meters and 
> feet), it wouldn't have crashed!
>
> The solution is called "Fahrenheit-Celsius" equating in the Rasch 
> literature. It can be encountered when different item types (MCQ, 
> T-F,  polytomies) are included in the same instrument. Or when the 
> same instrument is given in different situations, e.g., high-stakes 
> and low-stakes.
>
> Cordially,
> Mike L.
>
> At 6/2/2008, you wrote:
>> Mike. If there is a different unit, in principle the responses in 
>> frames of reference that have different units (due to different 
>> levels of discrimination) need to be modelled separately first then 
>> brought onto a common scale. Higher discrimination produces responses 
>> for which the Guttman pattern is more likely, other things being 
>> equal. I've shown cases in which differences in the levels of 
>> discrimination produce very misleading inferences in empirical 
>> situations if they are not dealt with appropriately.
>
> Mike Linacre
> Editor, Rasch Measurement Transactions
> rmt at rasch.org _www.rasch.org/rmt/_ <http://www.rasch.org/rmt/> Latest 
> RMT:  21:4 Spring 2008
>
> ------------------------------------------------------------------------
>
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