[Rasch] RSM & PCM

Purya Baghaei puryabaghaei at gmail.com
Fri Mar 12 19:25:40 EST 2010


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?

Regards

Purya


On Wed, Mar 10, 2010 at 2:52 PM, Rodney Staples
<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,
>
> Rod
>
>
>
>
>
>
>
> ___________________________________________________________________________
>
> Dr. Rodney Staples.
>
> e-mail: 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]*On
> Behalf Of *Thomas Salzberger
> *Sent:* Thursday, 11 March 2010 12:02 AM
> *To:* 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.
>
> Thomas
>
>
>
>  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
>
>
>
>
>  -----Inline Attachment Follows-----
>
> _______________________________________________
>
> Rasch mailing list
>
> Rasch at acer.edu.au <http://??.htm>
>
> https://mailinglist.acer.edu.au/mailman/listinfo/rasch
>
>  _______________________________________________
>
> Rasch mailing list
>
> Rasch at acer.edu.au
>
> https://mailinglist.acer.edu.au/mailman/listinfo/rasch
>
> _______________________________________________________
>
> 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
>
>
>
>  *"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.rasch2010.cbs.dk/
> <http://www.rasch2010.cbs.dk/>
>
> The Matilda Bay Club: 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>
>
> https://mailinglist.acer.edu.au/mailman/listinfo/rasch
>
> ------------------------------------------------- Please consider the
> environment before you print
>  ------------------------------------------------- Please consider the
> environment before you print
>
>
> _______________________________________________
> Rasch mailing list
> Rasch at acer.edu.au
> https://mailinglist.acer.edu.au/mailman/listinfo/rasch
>
>


-- 
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/20100312/1edc63b9/attachment.html 


More information about the Rasch mailing list