[Rasch] Re-calibration Procedure

John Barnard (EPEC) JohnBarnard at bigpond.com
Mon Jun 21 15:35:14 EST 2010

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 abilities.)

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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