[Rasch] RSM & PCM

David Torres Irribarra dti.berkeley at gmail.com
Sat Mar 13 06:56:39 EST 2010


Purya,

I believe it is possible to implement that model in Conquest, but you
would have to manually edit the design matrix. I have not personally
implemented that model, but I imagine that maybe you could export the
default design matrix that is used for a partial credit model and use
it as a starting point.

Regards,

David

On Fri, Mar 12, 2010 at 4:22 AM, David Andrich <david.andrich at uwa.edu.au> wrote:
> 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
>
>
>
>
>
> David Andrich  BSc, MEd (UWA), PhD (Chic) FASSA
>
> Chapple Professor
> david.andrich at uwa.edu.au
>
>
>
> Graduate School of Education
> The University of Western Australia
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> ________________________________
>
> 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?
>
> 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
>
>
>
> 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/
>
>
>
>
>
> -----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
>
>
>
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> _______________________________________________________
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> Dr. Thomas Salzberger
>
> http://www2.wu-wien.ac.at/marketing/user/salzberger/
>
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>
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>
> Email: Thomas.Salzberger at wu.ac.at, Thomas.Salzberger at gmail.com
>
>
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>
>
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> --
> Purya Baghaei, Ph.D
> English Department,
> Islamic Azad University,
> Ostad Yusofi Str.
> Mashad, Iran.
> Phone: +98 511 6634763
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-- 
Regards,

David

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