[Rasch] Fw: Re: [MBC-Rasch] Subtest Disordered threshold

Andrew Stephanou suremes at yahoo.com
Wed Sep 5 10:42:22 AEST 2018


----- Forwarded message -----
 From: David Andrich <david.andrich at uwa.edu.au>To: The Matilda Bay Club <rasch at wu.ac.at>Sent: Wednesday, 5 September 2018, 12:25:22 am AESTSubject: Re: [MBC-Rasch] Subtest Disordered threshold
 


Ali and colleagues in social measurement
 


Regarding Svend’s comment:
 


 “You should also be aware that the Rasch model itself does not require ordered thresholds and that you will find no mention of this in any of Rasch's writings.”
 


The Rasch model for ordered categories in the form of thresholds was not known to Rasch. And therefore, it is not surprising that he did not refer to them. (See a summary of where Georg Rasch and Ben Wright go to with the ordered category model in Andrich, 2013). However, taking the implication that if Rasch did not mention something explicitly that it should be ignored or is wrong would imply that we should not be even analysing data with the Rasch model expressed in terms of thresholds.
 


The work of Rasch was built on by Erling Andersen and myself to give the threshold form of the model as also explained in Andrich (2013).
 


Svend goes on to say “The requirement of ordered thresholds is an additional requirement that somebody else has added to Rasch's requirements of objective measurement. “
 


I am happy to say that I was the one that added that on, but only because of the implications of disordered thresholds. But I did not add it to the model. I added the requirement to the estimates of the thresholds as a reflection of a requirement of the data. To stress, the case for ordered threshold estimates is that they reveal and important property of the data.
 


Adding this requirement of the thresholds does not violate the invariance requirement and sufficiency of the model that is objectivity in Rasch’s terms. The reason I added it on is that if the threshold estimates are disordered, then whatever the context, and I will get to local dependence context below, the model shows that in applying it, the data violate the principles of elementary statistical inference. To stress it is an add-on to the requirement of data, not an add-on to the model. Svend implies (to me anyway) that if it some feature is not a property of the model, then it does not have to be a property of the data.
 


The elementary statistical inference is that of using a single number, e.g. mean, to characterise a distribution – this requires the distribution to be unimodal. One would not calculate the mean to summarise a bimodal distribution. Although Rasch did not talk about thresholds, he did not say that in applying models that follow from his theory of invariance, you should abandon elementary statistical inference.
 


If you form asuper-item from two other items, and the thresholds are severely reversed in thesuper-item, then there is severe local dependence (relative to the other items) in the data. Now this is a property of the set of data and if all items are kept together in the test, no analysis actually removes this dependence from the data. Forming a super-item improves fit because the model has absorbed the dependence in the threshold estimates. That is, dependence does not disappear, it just appears in the threshold estimates. As it happens fit is improved, but fit is not enough to conclude everything is now fine.
 


Let’s be concrete about the implication of severe dependence between two items. Suppose you have a set of 10 polytomous items scored 0 to 4, and that for some reason you form asuper-item from two of the items. You now have an item with possible scores 0 to 8. If the thresholds are severely reversed, then it is possible that a person’s distribution would show that the mean of the distribution is 4. Imagine 1000 people whose mean on these two items is 4. With reversed thresholds the proportion of scores of 1 and of 7 may both be much higher than the score of 4. This is a bimodal distribution. Are you happy to summarise these persons’ scores with 4 on these two items? If you are, you are happy to use the corresponding single person estimate in the Rasch model. However, this single estimate would say your long-term mean, if you imagine this person responding to this item many times, will be 4 even though on any given replication, the person is more likely to get a score of both 1 and 7. The dependence is pushing the possible scores to extremes.
 


Thus, I have to agree with Thomas. The context should be considered before being happy with a pair of items which have so much local dependence that thesuper-item formed from them has severely reversed thresholds, despite the fit improving and despite the estimates being able to be reversed. In the above case it maybe that one of the items is totally redundant. On the other hand, depending on the context you might want both items in the test, but you need to be careful in interpreting a total score.
 


Finally, Svend writes:
 


 “Of course, it is ok for you to agree with that, but the requirement of ordered thresholds does not extend tosuper-items summarizing responses to local dependent items.”
 


If you see that modelling the data is the end of the task, rather than understanding, explaining and improving items and a test, then of course having reversed thresholds is not a problem. The model formed with a super-item now shows better fit. But if you do not want to think that the mean score of 4 in the above case summarises a total score on two dependent items when the scores of 1 and 7 have much higher probabilities of occurring, even though the super-item fits, then you will see you have problems in the data revealed by modelling with the Rasch model.
 


Reference 
 


Andrich, D. (2013) The legacies of R. A. Fisher and K. Pearson in the application of the polytomous Rasch model for assessing the empirical ordering of categories. Educational and Psychological Measurement. 3(4), 553–580.
 
David




David Andrich, BSc MEd W.Aust., PhD Chic, FASSA
Chapple Professor david.andrich at uwa.edu.au
Graduate School of Education
The University of Western Australia
M428, 35 Stirling Highway, Crawley, 
Western AUSTRALIA, 6009
Telephone: +61 8 6488 1085;   Fax: +61 8 6488 1052 
GSE Psychometric Laboratory
http://www.education.uwa.edu.au/ppl/courses
www.matildabayclub.net


From: Rasch <rasch-bounces at wu.ac.at> on behalf of Ali Alnahdi <alialnahdi at KSU.EDU.SA>
Sent: Monday, 3 September 2018 5:19 PM
To: The Matilda Bay Club
Subject: Re: [MBC-Rasch] Subtest Disordered threshold 
Thanks a lot Svend
Ali Alnahdi, PT, PhDAssociate ProfessorRehabilitation Sciences DepartmentCollege of Applied Medical SciencesKing Saud UniversityP.O. Box 10219, Riyadh 11433Saudi ArabiaPhone:+966114693595http://fac.ksu.edu.sa/alialnahdi/homeFrom: Rasch <rasch-bounces at wu.ac.at> on behalf of Svend Kreiner <svkr at sund.ku.dk>
Sent: Monday, September 3, 2018 12:27:30 AM
To: The Matilda Bay Club
Subject: Re: [MBC-Rasch] Subtest Disordered threshold Dear Ali.

No. It is not required. It is well known that local dependence may create disordered thresholds in superitems. That is all according to the theory.

You should also be aware that the Rasch model itself does not require ordered thresholds and that you will find no mention of this in any of Rasch's writings. The requirement of ordered thresholds is an additional requirement, that somebody else has added to Rasch's requirements objective measurement. Of course, it is ok for you to agree with that, but the requirement of ordered thresholds does not extend to superitems summarizing responses to local dependent items.

Kind regards

Svend
________________________________________
From: Rasch [rasch-bounces at wu.ac.at] on behalf of Ali Alnahdi [alialnahdi at KSU.EDU.SA]
Sent: Sunday, September 02, 2018 4:15 PM
To: The Matilda Bay Club
Subject: [MBC-Rasch] Subtest Disordered threshold

Dear all
I am examining the fit of a locomotion scale that has 10 items (with 3 ordered response categories) using RUMM2030. The scale meets the requirements of the Rasch model except for the presence of response dependency between 2 items. Combining these 2 items into a subtest did address the issue of response dependency but the combined item (subtest) exhibit disordered threshold.
Is it required to have ordered threshold after combining items into subtest (super item)?? All the items (including the two item showing response dependency) had ordered threshold before combining the two items.

I would appreciate your inputs and thoughts
Ali Alnahdi



Ali Alnahdi, PT, PhD
Associate Professor
Rehabilitation Sciences Department
College of Applied Medical Sciences
King Saud University
P.O. Box 10219, Riyadh 11433
Saudi Arabia
Phone:+966114693595
http://fac.ksu.edu.sa/alialnahdi/home<https://mail.ksu.edu.sa/OWA/redir.aspx?C=Ee3h8A2alEaDwEIDB8qFBGr4mVpshc8I06r0u9ZcW2cWEWoelk5nZ_FdszeqQDh7KGjJqX5S2ZQ.&URL=http%3a%2f%2ffac.ksu.edu.sa%2falialnahdi%2fhome>
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