FW: [Rasch] Threshol Disordering

Stephanou, Andrew Stephanou at acer.edu.au
Tue Dec 19 13:04:58 EST 2006



From: David Andrich [mailto:D.Andrich at murdoch.edu.au] 
Sent: Tuesday, 19 December 2006 12:31 PM
To: rasch; The Matilda Bay Club
Cc: Stephanou, Andrew
Subject: RE: [Rasch] Threshol Disordering

Yes, but it is not simply that low frequencies in the middle categories
lead to reversed thresholds.  If the person distribution is bimodal for
some reason, (e.g. heights of adult men and woman), then the middle
categories, (e.g. around 5ft 7in) might have low frequencies.   Attached
is an example of a table of frequencies and the threshold estimates. As
you can see the middle categories have low frequencies, including a
category with zero frequency, yet the threshold estimates in both items
are properly ordered. It is also evident from the Figure that the person
distribution is bimodal, which leads to the middle categories having low
frequencies.  The data fit the  polytomous Rasch model. 
Thus the issue is why are there low frequencies in the middle
categories, not just that there are low frequencies.  In your case it is
most likely that some kind of dependence within each "item" is causing
the low frequencies in the middle categories and hence the reversed
The polytomous Rasch model accounts for this dependence. Thus the
analysis with the polytomous Rasch model is more relevant than analysis
in which the correct/incorrect responses within each passage are scored
dichotomously and analysed with the dichotomous Rasch model. Of course,
this is just a statistical diagnostic.  For understanding the dependence
and other factors it is necessary to consider the substantive issues,
not just the statistical.


From: rasch-bounces at acer.edu.au [mailto:rasch-bounces at acer.edu.au] On
Behalf Of Mike Linacre (RMT)
Sent: Monday, 18 December 2006 10:51 PM
To: rasch at acer.edu.au
Subject: Re: [Rasch] Threshol Disordering

Dear Anthony et al.:

Reversed Rasch-Andrich thresholds indicate low probabilities of
intermediate categories. These usually correspond to relatively low
frequencies of those categories in the data. So, in your items, some of
the 26 categories (item scores of 0-25) have relatively low frequencies.
If you examine the right-wrong scoring patterns across the missing words
within each item, it is likely that some patterns are much more frequent
than others, indicating dependencies among those missing words. These
dependencies lead to item scores with higher and lower frequencies, and
so to reversed thresholds.

Mike L.

At 12/18/2006, you wrote:

	Dear List members,
	  I'd be thankful for your expert comments on this.
	  I have Rasch analysed a language test which is called the
	test". It has the following form:
	  "The English language today _____ many distinct centres, 
	self-governing ____ with their own standards. The two ____
important are, of ____, 
	the United Kingdom in terms of ____, and the United States in
____ of 
	population. ......."
	  The students are to supply the missing words in the text.
There are 4 
	texts and each have 25 gaps.
	  I have used rating scale model. Each text is a polytomous item
	25 categories.
	  There is disordering in the thresholds of the test (but not in
	average measures).
	  How can this be interpreted in the context of a cloze test? 
	  Thanks in adavnce

Mike Linacre
Editor, Rasch Measurement Transactions
rmt at rasch.org www.rasch.org/rmt/ <http://www.rasch.org/rmt/>  Latest
RMT:  20:2 Autumn 

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