[Rasch] Re-calibration Procedure

ranganaths ranganath.s at excelindia.com
Mon Jun 21 15:57:20 EST 2010



            Thanks for the response and for the information on linking of
items. Can u please share a document for the equating process to get the
item re-calibrated on subsequent administration for all the 3 models. Thanks
once again.



Ranganath S



From: John Barnard (EPEC) [mailto:JohnBarnard at bigpond.com] 
Sent: Monday, June 21, 2010 11:05 AM
To: 'ranganaths'; rasch at acer.edu.au
Subject: RE: [Rasch] Re-calibration Procedure


Dear Ranganath


This is quite a mouth full! It is not only for CAT, but for all serious item
banking work. If you use classical statistics and calculate the item
difficulty and discrimination (point biserial correlation) you will have
some sample dependent information. However, these can change significantly
if you administer the same item to another cohort in another test. To
counter this, equating is needed. Although classical equating methods yield
some results, modern test theory is much more robust and sophisticated.


After administration of a test you do a calibration, i.e. derive item
difficulty estimates and person ability estimates. Depending on which model
you use, you will get one, two, three parameters for each item and ability
estimates relative to this on the same scale. Be careful, Rasch usually
standardises on item difficulty and IRT models on person ability. You cannot
simply cross over to another model once you have calibrated one data set.
The problem is that this scale is "unique" so if you calibrate some items
with some other items in a second administration, the common items will have
different parameters. An equating process is required to get them on a
common scale. This is how you build an item bank on one scale so that you
can use any subset of items to obtain comparable ability estimates. You can
see that it is not simply a process of taking the average!


CAT is a different ball game - it is a sophisticated application which
requires items to be on a common scale. It is an efficient way to administer
less items without compromising precision. In "conventional" testing, if you
want to compile different tests and compare abilities (performance), the
items in the bank you use must have been equated to a common scale or you
have to do the equating afterwards with common items, people or an external
exercise. (We actually talk about the linking of items and equating of






Prof John J Barnard (DEd;PhD;EdD)
Executive Director: EPEC Pty Ltd
CEO: CAT Measures Pty Ltd
ASC: Asia, Africa and Australia
Honorary Faculty UCT; Adj. USyd

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-----Original Message-----
From: rasch-bounces at acer.edu.au [mailto:rasch-bounces at acer.edu.au] On Behalf
Of ranganaths
Sent: Monday, 21 June 2010 3:13 PM
To: rasch at acer.edu.au
Subject: [Rasch] Re-calibration Procedure



            It is well known that in the case of CAT, for the item to be
included in the item bank, It needs to be calibrated and this happens over a
period of time on administering the item in various tests. Say for eg, we
have administered test1, test2.  testn the same question Q1. The item Q1
gets item parameter value a1,b1 and c1 in test1. The response vector being
v1 for the item Q1 in test1. In the successive tests should the response
vectors(v1,v2 . vn) for the same item Q1 be merged with the previous test
response to get the calibrated value of a1, b1 and c1.




Is it enough to have the a1, b1 and c1 value and then proceed having similar
values for the item in different tests and then take average of the
corresponding values to arrive at the final a, b and c values.




Ranganath S

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