[Rasch] RSM & PCM

Anthony James luckyantonio2003 at yahoo.com
Wed Mar 10 23:43:29 EST 2010


Thanks Thomas,
It seems that these are just a set of  assumptions 
that we have about our data. I was under the impression that when we 
talk about unequal distances either within or across the items we model 
the distances and weight them accordingly. That is, each category gets a
 different score depending on its difficulty. Something along these 
lines. I think there are some models which requie this, aren't there?
So
 we do not need to have such complicated modelling.
We just choose 
the type of the analysis depending on what we think of our data. Right?
Anthony

--- On Wed, 3/10/10, Anthony James <luckyantonio2003 at yahoo.com> wrote:

From: Anthony James <luckyantonio2003 at yahoo.com>
Subject: Re: [Rasch] RSM & PCM
To: "Thomas Salzberger" <thomas.salzberger at gmail.com>
Date: Wednesday, March 10, 2010, 6:42 AM

Thanks Thomas,
It seems that these are just a set of  assumptions that we have about our data. I was under the impression that when we talk about unequal distances either within or across the items we model the distances and weight them accordingly. That is, each category gets a different score depending on its difficulty. Something along these lines. I think there are some models which requie this, aren't there?
So we do not need to have such complicated modelling.
We just choose the type of the analysis depending on what we think of our data. Right?
Anthony

--- On Wed, 3/10/10, Thomas Salzberger <thomas.salzberger at gmail.com> wrote:

From: Thomas Salzberger <thomas.salzberger at gmail.com>
Subject: Re:
 [Rasch] RSM & PCM
To: rasch at acer.edu.au
Date: Wednesday, March 10, 2010, 6:13 AM


 
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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