[Rasch] RSM & PCM

Thomas Salzberger thomas.salzberger at gmail.com
Sat Mar 13 01:24:13 EST 2010


At 13:22 12.03.2010, David Andrich wrote:
>Content-Language: en-US
>Content-Type: multipart/alternative;
> 
>boundary="_000_957CC9D8A146604BAA2EE76E83DA1C6E18F0A593ITSWIN009staffa_"
>
>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.



Winmira by von Davier was (is?) able to estimate 
various parameterisations, including the 
equidistant one. I do not know whether it is still available or updated.

Thomas


>Hope that helps.
>
>David
>
>
>
>
>
>David Andrich  BSc, MEd (UWA), PhD (Chic) FASSA
>
>Chapple Professor
><mailto:david.andrich at uwa.edu.au>david.andrich at uwa.edu.au
>
>
>
>Graduate School of Education
>The University of Western Australia
>M428, 35 Stirling Highway,
>
>Crawley,
>
>Western Australia , 6009
>
>AUSTRALIA
>
>Telephone: +61 8 6488 1085
>Fax: +61 8 6488 1052
>www.gse.uwa.edu.au
>CRICOS Code: 00126G
>
><blocked::http://www.education.uwa.edu.au/ppl>Pearson Psychometric Laboratory
>
>http://www.education.uwa.edu.au/ppl/courses
>
><http://www.matildabayclub.net>www.matildabayclub.net
>
>www.rasch2010.cbs.dk
>
>
>
>----------
>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 
><<mailto:rodstaples at ozemail.com.au>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/%7Erodstaples/Measurement3.htm>http://members.ozemail.com.au/~rodstaples/Measurement3.htm 
>
>
>
>
>Hope this helps,
>
>Rod
>
>
>
>
>
>
>
>___________________________________________________________________________
>
>Dr. Rodney Staples.
>
>e-mail: <mailto:rodstaples at ozemail.com.au>rodstaples at ozemail.com.au
>
>Telephone: +61 3 9770 2484
>
>Mobile: +61 4 1935 9082
>
>Web: 
><http://members.ozemail.com.au/%7Erodstaples/>http://members.ozemail.com.au/~rodstaples/
>
>
>
>
>
>-----Original Message-----
>From: 
><mailto:rasch-bounces at acer.edu.au>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: <mailto:rasch at acer.edu.au>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 
><<mailto:thomas.salzberger at gmail.com>thomas.salzberger at gmail.com> wrote:
>
>From: Thomas Salzberger 
><<mailto:thomas.salzberger at gmail.com>thomas.salzberger at gmail.com>
>
>Subject: Re: [Rasch] RSM & PCM
>
>To: <mailto:rasch at acer.edu.au>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 
><<mailto:luckyantonio2003 at yahoo.com>luckyantonio2003 at yahoo.com> wrote:
>
>From: Anthony James 
><<mailto:luckyantonio2003 at yahoo.com>luckyantonio2003 at yahoo.com>
>
>Subject: [Rasch] RSM & PCM
>
>To: <mailto:rasch at acer.edu.au>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
>
><http://??.htm>Rasch at acer.edu.au
>
>https://mailinglist.acer.edu.au/mailman/listinfo/rasch
>
>_______________________________________________
>
>Rasch mailing list
>
><mailto:Rasch at acer.edu.au>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://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>http://www.wu.ac.at/mm/team/salzberg
>
>Email: 
><mailto:Thomas.Salzberger at wu.ac.at>Thomas.Salzberger at wu.ac.at, 
><mailto:Thomas.Salzberger at gmail.com>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>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/
>
>The Matilda Bay Club: 
><http://www.matildabayclub.net/>http://www.matildabayclub.net
>
>Rasch Courses: 
><http://www.education.uwa.edu.au/ppl/courses>http://www.education.uwa.edu.au/ppl/courses, 
>http://home.btconnect.com/Psylab_at_Leeds/
>
>der markt - Journal für Marketing: 
><http://www.springer.com/dermarkt>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>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
>
><http://mc/compose?to=Rasch@acer.edu.htm>Rasch at acer.edu.au
>
>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
><mailto:Rasch at acer.edu.au>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
>
>_______________________________________________
>Rasch mailing list
>Rasch at acer.edu.au
>https://mailinglist.acer.edu.au/mailman/listinfo/rasch

-------------------------------------------------
Please consider the environment before you print
-------------- next part --------------
An HTML attachment was scrubbed...
URL: https://mailinglist.acer.edu.au/pipermail/rasch/attachments/20100312/c3a3fd82/attachment.html 


More information about the Rasch mailing list