[Rasch] Re: Rasch Digest, Vol 35, Issue 12

Juanito Talili talilij at yahoo.com
Mon Jun 23 11:26:27 EST 2008


Thank you for your reply, Steve and Tomas.
 
Just some follow-up questions:
 
1. For each item (or person), Rasch provides m-1 thresholds for the m response categories.  The arithmetic mean of the m-1 thresholds for each item(person) is then the item (or person) location or commonly called item (or person) measure.  Am I right?
 
2. If we call the item measure as "item endorsability", how do we call the person measure?
3. What is your idea about the infit and outfit for each measure?
4. Relative to the instrument, how do we interpret the item and person separation and reliability?
 
Thank you.
J. Talili
 


--- On Sun, 6/22/08, Fraser Rew <Fraser.Rew at nzqa.govt.nz> wrote:

From: Fraser Rew <Fraser.Rew at nzqa.govt.nz>
Subject: [Rasch] Re: Rasch Digest, Vol 35, Issue 12
To: rasch at acer.edu.au
Date: Sunday, June 22, 2008, 11:40 PM

Picking up on Steve Humphry's comments, my understanding (and I'm a
relative newcomer to all this so someone may need to correct me) is that
in the item difficulty for each of the responses is the point at which
that response or a higher one becomes more likely than any lower
response, rather than being simply the point at which they cross. In the
dichotomous case these two are obviously the same; in the polytomous
case they are not. 

Looking at examination data we have found many cases, particularly
where the difficulty of two adjacent items is similar or (using the
two-parameter model) that the discrimination is low that the crossing
point is actually well removed from the difficulty parameter. In some
cases a given response is not the most likely for ANY ability score and
in these cases the curve's crossing point for the higher grade will
clearly be at a lower ability score than its crossing point in the lower
grade. As a digression we weren't able to directly calculate crossing
points based on item parameters, and used Newton-Raphson instead.

In practice the difference between the parameter and the crossing point
is often negligible, but in many cases it can be surprisingly large.

Regards

Fraser

Fraser Rew
Researcher/Data Analyst
Qualificiations Division
DDI: 04 463 4368
Extn: 4368

www.nzqa.govt.nz

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Today's Topics:

   1. Measures in Rasch Model (Juanito Talili)
   2. Re: Measures in Rasch Model (Thomas Salzberger)
   3. Re: Measures in Rasch Model (Stephen Humphry)


----------------------------------------------------------------------

Message: 1
Date: Fri, 20 Jun 2008 20:26:01 -0700 (PDT)
From: Juanito Talili <talilij at yahoo.com>
Subject: [Rasch] Measures in Rasch Model
To: rasch at acer.edu.au 
Message-ID: <963004.46958.qm at web46205.mail.sp1.yahoo.com>
Content-Type: text/plain; charset="iso-8859-1"

Dear Rasch Modelers,
á
For a dichotomous case, the item measure is called "item difficulty"
while the person measure is called "person ability".á I have a
difficulty of understanding the measuresáfor theápolytomous(rating
scale)ácase.á Can somebody have a kind heart to explain these things?
á
Thank you.
J. Talili


      
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Message: 2
Date: Sat, 21 Jun 2008 14:47:26 +0200
From: Thomas Salzberger <Thomas.Salzberger at wu-wien.ac.at>
Subject: Re: [Rasch] Measures in Rasch Model
To: rasch at acer.edu.au 
Message-ID: <20080621144726.jn0yubnd6kgcg0cw at imp.wu-wien.ac.at>
Content-Type: text/plain;	charset=ISO-8859-1;	DelSp="Yes";
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Quoting Juanito Talili <talilij at yahoo.com>:

> Dear Rasch Modelers,
>  For a dichotomous case, the item measure is called "item  
> difficulty"  while the person measure is called "person
ability".  I 

> have a  difficulty of understanding the measures for the  
> polytomous(rating  scale) case.  Can somebody have a kind heart to  
> explain these things?
>  Thank you.
> J. Talili

Juanito,

what is the item difficulty (delta) in a dichotomous item? It is the  
location on the latent continuum where a positive response  
(correct/affirmative answer, coded 1) and a negative response (coded  
0) have the same probability. Below that point (beta < delta) a  
negative response is more likely and above that poi
nt (beta > delta) a 

positive answer is more likely. So, it is a transition point where  
(going from minus infinity to plus infinity) the most likely response 

changes from 0 to 1. For two responses to distinguish between one item 

parameter is needed. This parameter is the threshold between response 

0 and response 1.

Generalising this idea to the polytomous case is relatively  
straighforward. If you have three response options, two such  
transition points (thresholds) have to be modelled. With m categories, 

you need m-1 thresholds to be modelled and that, of course, is done by 

the threshold parameters. Consequently, the interpretation of the item 

location in the dichotomous case and the threshold parameters in the  
polytomous model is, in principle, the same.

Since a set of, say, six thresholds (needed for a seven category  
response scale) is a little bit hard to handle if you compare items,  
it is quite common to calculate the mean of the item's threshold and  
interpret it as a sort of overall-difficulty. If your items have all  
have a similar spread of threshold locations (in the rating scale  
model they have the same by definition) this should be okay. If  
thresholds vary considerably between items the overall location can be 

misleading.

In the context of item difficulty, I also want to point out that the  
term difficulty makes many, uninitiated, people think the Rasch model 

(or IRT models in general) can only be applied to achievement tests. I 

don't know what field of science you are in, but I can tell you that  
in marketing research, where we are mostly concerned with attitudinal 

or attitude-like constructs, it can be hopeless to explain people that 

item difficulty is a technical term and that it should not always be  
interpreted literally. Using a neutral term like 'item location' or  
something like endorsability may help convey the idea.

Thomas
_______________________________________________________
Dr. Thomas Salzberger
╓sterreichische Gesellschaft fⁿr Absatzwirtschaft
c/o WU Wien - University of Economics and Business, Vienna
Department of Marketing, Institute of Marketing Management
(WirtschaftsuniversitΣt Wien, Institut fⁿr Marketing-Management)
Augasse 2-6, 1090 Wien
Email: Thomas.Salzberger at gmail.com, Thomas.Salzberger at wu-wien.ac.at 
WWW: http://www2.wu-wien.ac.at/marketing/user/salzberger/ 
MBC: http://www.matildabayclub.net 



------------------------------

Message: 3
Date: Sat, 21 Jun 2008 20:55:21 +0800
From: Stephen Humphry <shumphry at cyllene.uwa.edu.au>
Subject: Re: [Rasch] Measures in Rasch Model
To: rasch at acer.edu.au 
Message-ID: <20080621205521.vxps3diask0wcc84 at webmail-2.ucs.uwa.edu.au>
Content-Type: text/plain;	charset=ISO-8859-1;	DelSp="Yes";
	format="flowed"


Hi. For dichotomous items, there is a single threshold at which it is 

equally probably a person will respond incorrectly or correctly. This 

threshold is the item difficulty.

For polytomous item, the item parameters are also thresholds. Each  
threshold is the location at which it is equally likely a person's  
response will be in one of two adjacent categories, or be judged in  
one of two adjacent categories. At the first threshold, the scores 0  
and 1 are equally likely, at the second threshold, the scores 1 and 2 

are equally likely, and so on.

The polytomous model is sometimes written with an item difficulty and 

parameters that represent the distance of each threshold from the item 

difficutly. In this case, item difficulty is by definition the average 

threshold location.

However, to understand how the parameters of the polytomous model are 

an extension of the single parameter of the dichotomous model, it is  
probably simpler for you to think about one threshold (item  
difficulty) for dichotomous items, and more than one threshold for  
polytomous items with 3 or more categories.

Item difficulty is simply the single threshold in the special case in 

which there is only
 one threshold and two categories, such as  
incorrect and correct responeses. Different terms may be used to refer 

to the thresholds but the concept remains the same whatever these  
parameters are called.

Hope that helps,

Steve


Quoting Juanito Talili <talilij at yahoo.com>:

> Dear Rasch Modelers,
> á
> For a dichotomous case, the item measure is called "item
difficulty" 

> while the person measure is called "person ability".á I have a 

> difficulty of understanding the measuresáfor theápolytomous(rating  
> scale)ácase.á Can somebody have a kind heart to explain these
things?
> á
> Thank you.
> J. Talili
>
>
>





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