# [Rasch] FW: c-parameter

Mark Moulton markhmoulton at gmail.com
Mon Jun 4 07:30:27 EST 2012

```Dear Margaret,

to me.

Mark Moulton

On Sun, Jun 3, 2012 at 3:27 AM, Margaret Wu <wu at edmeasurement.com.au> wrote:

> 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.****
>
> ** **
>
> Margaret**
>
> ** **
>
> *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 www.rasch.org/rmt/ Latest RMT: 25:4 Spring 2012****
>
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