[Rasch] RSM & PCM

Thomas Salzberger thomas.salzberger at gmail.com
Wed Mar 10 23:13:54 EST 2010


Anthony,

let us assume we have a four category item, so 
there are three thresholds (0/1, 1/2 and 2/3, 
referred to as tau1, tau2 and tau3, respectively)
In the Rating scale model, the distance between 
the thresholds tau1 and tau2 does NOT need to be 
equal to the distance between tau2 and tau3.
But the difference between tau1 and tau2 has to 
be equal across all items. Likewise the 
difference between tau2 and tau3 has to be the same for all items.
So, no restrctions within the item but restrictions across items.

In other words, in the PCM, each item has its own 
rating scale structure, while in the rating scale 
model we have a common rating scale structure across all items.
The RSM is therefore more restrictive. Whether 
the PCM fits statistically significantly better 
than the RSM can be tested by a likelihood ratio test.

What you have in mind, a model where all 
distances between pairs of adjacent thresholds 
are equal, would be even more restrictive than the RSM.


At 12:39 10.03.2010, Anthony James wrote:
>I was just wondering how PCM accomodates unequal 
>distances when we do not model them.

I am sorry, I don't get this statement. When we 
do not model unequal distances (across items), 
i.e. we model equal distances, we do not apply the PCM.


>We just sum up correct responses on each polytomy and analyse it.


We always do that. If it's a Rasch model, then raw score sufficiency holds.


Thomas

>A sum score is in fact given to the analysis and 
>not modelled distances among items. Doesn't here a PCM reduce to an RSM?
>Cheers
>Anthony
>
>--- On Wed, 3/3/10, Anthony James <luckyantonio2003 at yahoo.com> wrote:
>
>From: Anthony James <luckyantonio2003 at yahoo.com>
>Subject: [Rasch] RSM & PCM
>To: rasch at acer.edu.au
>Date: Wednesday, March 3, 2010, 2:17 AM
>
>
>
>--
>
>Dear All,
>
>I know that this is a very old and probably a 
>boring question for many of you. But I need to know this
>
>What is the difference between rating  scale model and partial credit model?
>
>What I have gathered is that in RSM the 
>distances between the points on the scale is 
>equal and this distance is the same for all the 
>items in the instrument. That is, the ability 
>difference needed to endorse 3 rather than 2 is 
>the same as the ability difference needed to endorse 5 rather than 4. Right?
>
>In PCM, however, the distances between points on 
>the scale is unequal  both within the items and 
>between the items in the instrument. That is, 
>the ability increment to score 3 on an item 
>rather than 2 is not the same as the ability 
>increment needed to score 6 rather than 5. And 
>these distances are unequal among  the items in the test. Right?
>
>
>Cheers
>
>Anthony
>
>
>
>
>
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_______________________________________________________
Dr. Thomas Salzberger
http://www2.wu-wien.ac.at/marketing/user/salzberger/
http://www.wu.ac.at/statmath/faculty_staff/lecturer/salzberger
http://www.wu.ac.at/mm/team/salzberg
Email: Thomas.Salzberger at wu.ac.at, Thomas.Salzberger at gmail.com



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