[Rasch] RSM & PCM

David Andrich david.andrich at uwa.edu.au
Fri Mar 12 23:22:56 EST 2010

Purya. I am surprised that you were able to find that article. First I regret calling that parameterization of the general polytomous, unidimensional Rasch model as a model - it is just a particular parameterization, just as is the partial credit and rating scale a parameterizations are that too.
Second, like all models and parameterizations, they may not be practical. However, the point of that paper was to summarize quickly whether or not, in explicit quantitative terms, there was any local dependence.

Finally, RUMM does have that parameterization as a particular option for analysis. I do not know about other programs.
Hope that helps.

David Andrich  BSc, MEd (UWA), PhD (Chic) FASSA
Chapple Professor
david.andrich at uwa.edu.au<mailto:david.andrich at uwa.edu.au>

Graduate School of Education
The University of Western Australia
M428, 35 Stirling Highway,
Western Australia , 6009

Telephone: +61 8 6488 1085
Fax: +61 8 6488 1052
CRICOS Code: 00126G
Pearson Psychometric Laboratory<blocked::http://www.education.uwa.edu.au/ppl>

From: rasch-bounces at acer.edu.au [mailto:rasch-bounces at acer.edu.au] On Behalf Of Purya Baghaei
Sent: Friday, 12 March 2010 4:26 PM
To: rasch at acer.edu.au
Subject: Re: [Rasch] RSM & PCM

Anthony and Thomas,
Andrich (1985) proposed a model called "equidistant" or DLIM model, I think. This model assumes that the distances between the thresholds within the items are equal but not necessarily across the items. The model was suggested to account for local dependency in educational tests where several items are based on one prompt by forming testlets. The assumption of equal distances between thresholds within items in educational tests sounds rather impractical. I'm not sure if it's implemented in any software. Does anyone out there know of a Rasch programme that fits equidistant model? Or is it possible to fit the model with some command statements in Winsteps, ConQuest or RUMM?

On Wed, Mar 10, 2010 at 2:52 PM, Rodney Staples <rodstaples at ozemail.com.au<mailto:rodstaples at ozemail.com.au>> wrote:
Hi Anthony and Thomas,
There is a very full discussion of the distinction between Likert scales and Rasch Partial Credit models in Bond And Fox, Applying the Rasch Model, Chapter 6.

A different example drawn from a satisfaction survey is on my site at: http://members.ozemail.com.au/~rodstaples/Measurement3.htm<http://members.ozemail.com.au/%7Erodstaples/Measurement3.htm>

Hope this helps,


Dr. Rodney Staples.

e-mail: rodstaples at ozemail.com.au<mailto:rodstaples at ozemail.com.au>

Telephone: +61 3 9770 2484

Mobile: +61 4 1935 9082

Web: http://members.ozemail.com.au/~rodstaples/<http://members.ozemail.com.au/%7Erodstaples/>

-----Original Message-----
From: rasch-bounces at acer.edu.au<mailto:rasch-bounces at acer.edu.au> [mailto:rasch-bounces at acer.edu.au<mailto:rasch-bounces at acer.edu.au>]On Behalf Of Thomas Salzberger
Sent: Thursday, 11 March 2010 12:02 AM
To: rasch at acer.edu.au<mailto:rasch at acer.edu.au>
Subject: Re: [Rasch] RSM & PCM

At 13:42 10.03.2010, you wrote:
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?

That is exactly right. Sometimes a common rating scale makes sense. One could at least try it.
Obviously it does not make sense when the categories are worded differently and it is impossible to run the RSM when the number of categories varies.
(That said, you can actually have several RSMs within your instrument with some items sharing a common rating scale structure and others not.)

The important thing is that weighting category scores (or, in general, item scores) is never related to the difficulty of an item (we do not weight difficult dichotomous items higher than easy ones). This is always the case, even in general IRT.

Weighting refers to discrimination. In the 2pl, items are weighted differently because of different discrimination, not because of different difficulty.

In the RSM as well as in the PCM, the discrimination is assumed to be equal as this is a key property of the Rasch model.
However, in the PCM this fact is somewhat obscured by the fact that different threshold distances between items lead to ICCs which do intersect.
But at the level of each threshold, the latent response curves are in fact parallel.

If it helps to illustrate the last point, I might send you a graph from RUMM which illustrates this nicely.



--- On Wed, 3/10/10, Thomas Salzberger <thomas.salzberger at gmail.com<mailto:thomas.salzberger at gmail.com>> wrote:
From: Thomas Salzberger <thomas.salzberger at gmail.com<mailto:thomas.salzberger at gmail.com>>
Subject: Re: [Rasch] RSM & PCM
To: rasch at acer.edu.au<mailto:rasch at acer.edu.au>
Date: Wednesday, March 10, 2010, 6:13 AM
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.

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?
--- On Wed, 3/3/10, Anthony James <luckyantonio2003 at yahoo.com<mailto:luckyantonio2003 at yahoo.com>> wrote:
From: Anthony James <luckyantonio2003 at yahoo.com<mailto:luckyantonio2003 at yahoo.com>>
Subject: [Rasch] RSM & PCM
To: rasch at acer.edu.au<mailto: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?

-----Inline Attachment Follows-----
Rasch mailing list
Rasch at acer.edu.au<http://??.htm>
Rasch mailing list
Rasch at acer.edu.au<mailto:Rasch at acer.edu.au>
Dr. Thomas Salzberger
Email: Thomas.Salzberger at wu.ac.at<mailto:Thomas.Salzberger at wu.ac.at>, Thomas.Salzberger at gmail.com<mailto:Thomas.Salzberger at gmail.com>

"You can exist without wine but you cannot live..." Jack Mann

Measurement in Marketing - An alternative framework: http://www.e-elgar-business.com/Bookentry_DESCRIPTION.lasso?id=13315
Copenhagen 2010 International Conference on Probabilistic Models for Measurement: http://www.matildabayclub.net<http://www.matildabayclub.net/> , http://www.rasch2010.cbs.dk/ <http://www.rasch2010.cbs.dk/>
The Matilda Bay Club: http://www.matildabayclub.net<http://www.matildabayclub.net/>
Rasch Courses: http://www.education.uwa.edu.au/ppl/courses, http://home.btconnect.com/Psylab_at_Leeds/ <http://home.btconnect.com/Psylab_at_Leeds/>
der markt - Journal für Marketing: http://www.springer.com/dermarkt
Präferenzanalyse mit R @ Amazon: http://www.amazon.de/Pr%C3%A4ferenzanalyse-mit-Anwendungen-Behavioural-Management/dp/3708903854/ref=sr_1_2?ie=UTF8&s=books&qid=1243162762&sr=1-2 ------------------------------------------------- Please consider the environment before you print
-----Inline Attachment Follows-----
Rasch mailing list
Rasch at acer.edu.au<http://mc/compose?to=Rasch@acer.edu.htm>
------------------------------------------------- Please consider the environment before you print
------------------------------------------------- Please consider the environment before you print

Rasch mailing list
Rasch at acer.edu.au<mailto:Rasch at acer.edu.au>

Purya Baghaei, Ph.D
English Department,
Islamic Azad University,
Ostad Yusofi Str.
Mashad, Iran.
Phone: +98 511 6634763

Please consider the environment before you print
-------------- next part --------------
An HTML attachment was scrubbed...
URL: https://mailinglist.acer.edu.au/pipermail/rasch/attachments/20100312/e7949aa5/attachment.html 

More information about the Rasch mailing list