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

Stephen Humphry stephen.humphry at uwa.edu.au
Tue Jun 3 12:29:37 EST 2008


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  <http://www.rasch.org/rmt/> www.rasch.org/rmt/ Latest RMT:
21:4 Spring 2008 

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