[Rasch] FW: c-parameter

David Andrich david.andrich at uwa.edu.au
Mon Jun 4 13:31:27 EST 2012

Margaret. It might help if you define discrimination for a partial credit item? We know the discrimination in dichotomous item. I am not sure the two are compatible. Also, what is your formulation of a "generalized 2-parameter analysis"?  Maybe you can give us the equation in an attachment.



David Andrich, BSc MEd W.Aust., PhD Chic, FASSA
Chapple Professor
david.andrich at uwa.edu.au<mailto:david.andrich at uwa.edu.au>

Graduate School of Education
The University of Western Australia
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Telephone: +61 8 6488 1085
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Pearson Psychometric Laboratory<blocked::http://www.education.uwa.edu.au/ppl>
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From: rasch-bounces at acer.edu.au [mailto:rasch-bounces at acer.edu.au] On Behalf Of Margaret Wu
Sent: Sunday, 3 June 2012 6:27 PM
To: rasch at acer.edu.au
Subject: [Rasch] FW: c-parameter

Rense writes: One down (guessing), one to go (discrimination)
Mike writes: Answer: OPLM with its fixed, but different, discrimination coefficients. http://www.cito.com/research_and_development/pyschometrics/psychometric_software/oplm.<http://www.cito.com/research_and_development/pyschometrics/psychometric_software/oplm.aspx>
There isn't such a divide between the Rasch model and the two parameter model. Let's consider an example. Suppose we have three Rasch partial credit items. Item 1 has scores 0,1,2,3,4. Item 2 has scores 0,1,2, and Item 3 has scores 0,1. So Item 1 has the highest weight in the test. That is, Item 1 has twice the weight of Item 2 (it counts 4 points in the test, while Item 2 only counts 2 points), and four times the weight of Item 1 in the test. How does one decide on the weight of a partial credit item? Or, the question could be, how does one decide on the maximum score of an item? Contrary to common perception that the maximum score of a partial credit relates to its difficulty, actually the maximum score of an item (or the weight of an item) depends on its discrimination. This makes sense. If an item does not discriminate, we want to weigh it down in the test. If an item discriminates highly, we want to increase the weight of the item in the test.

Suppose we run a generalized 2-parameter analysis, the scores of Item 1 may come out to be 0,  0.8,  1.1, 1.7, 2.2. These scores suggest that, instead of scoring Item 1 with 0, 1, 2, 3, 4, we should score these five categories as 0,  0.8,  1.1, 1.7, 2.2. Because the scores are not integer, we no longer have the Rasch model. However, if we round the scores to integers, and score the five categories, 0, 1, 1, 2, 2, (that is, we collapse original categories 1 and 2 as 1, and collapse categories 3 and 4 as 2), our new partial credit scoring is now 0, 1, 2. This is still a Rasch partial credit item. The consequence of this re-scoring will make the item fit the Rasch model better, and potentially increase the test reliability, because now we put more weight on "good" items (more discriminating ones), and less weight on "poor" items, and we still stay in the Rasch family.

In practice, many of us using the Rasch model have already been doing this. We examine the item analysis and decide on how to re-score or collapse categories to improve fit and reliability, without actually running a 2-parameter model . What we are doing is already trying to find the best weight for each item. So whenever you are using Rasch partial credit model, you are already giving different items different weights, so, in fact, you are already moving into the 2-parameter model concept.

The technical difference between a 2-parameter model and a Rasch partial credit model is that for a partial credit model, the category scores must be integer and there must not be jumps (e.g., we can't have 0,1,3,4). The 2-parameter model allows for non-integer scores. But by rounding the scores, you can have the best of the two worlds, and that's how OPLM can bring the best out of the one-parameter model.

Certainly, whenever you are using Rasch partial credit models, you are already using a special case of the 2-parameter model. We should realize that when items have different maximum scores, you are already providing different weights to the items, and that's the idea of 2-parameter models. But we can still stay within the Rasch family when we incorporate the item discrimination information.


From: rasch-bounces at acer.edu.au [mailto:rasch-bounces at acer.edu.au] On Behalf Of Mike Linacre
Sent: Sunday, 3 June 2012 5:29 AM
To: rasch at acer.edu.au
Subject: Re: [Rasch] c-parameter

Rense writes: One down (guessing), one to go (discrimination)

Answer: OPLM with its fixed, but different, discrimination coefficients. http://www.cito.com/research_and_development/pyschometrics/psychometric_software/oplm.<http://www.cito.com/research_and_development/pyschometrics/psychometric_software/oplm.aspx>aspx

<http://www.cito.com/research_and_development/pyschometrics/psychometric_software/oplm.aspx>Mike L.

Mike Linacre
rmt at rasch.org<mailto:rmt at rasch.org> www.rasch.org/rmt/<http://www.rasch.org/rmt/> Latest RMT: 25:4 Spring 2012
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