[Rasch] Comparison Rasch 3-parm IRT

Agustin Tristan ici_kalt at yahoo.com
Sun Sep 15 23:25:11 EST 2013

```Hello.

Ricardo: "It is interesting that then both models will tell the same history about the subjects" and that

Mike: "... Wright... concluded...  that 3PL ability estimates and item difficulties are statistically equivalent to Rasch measures",

then I can imagine  that the Rasch model and 3PL are equivalent. Why bother about measuring and making scales and other conceptual discussions?

This gives me the idea to prefer 3PL because:

(a) people like to describe the data ---- Rasch model is not descriptive
(b) can obtain discrimination and pseudo-guessing parameters ---- Rasch model does not permit to determine those parameters
(c) it is the same history about subjects than what is supposed to get with the Rasch model --- then why not use the item description and 3PL parameters?

Fortunately, Svend explains two things against these 3 preferences:

(1) 3pl estimates and Rasch estimates are "equivalent" if items actually fit the Rasch model

It should be evident to every 3PL user that (1) is necessary and in this case they should obtain
c = 0 or very close and a constant value for a, close to the equivalent for the Rasch curve.

(2) If items do not fit the Rasch model, the two sets of estimates can not be expected to be equivalent...you should not use Rasch estimates anyway
It should be evident to every 3PL user that items that do not fit the Rasch model should not be used even if the 3 parameters can be calculated in any case and under any circumstance. An also that even for items fitting the Rasch model, it is necessary to prove content validity, that the scale is working fine, that item-test correlation is positive and high... and certainly many more things. My impression is that 3 PL users prefer to obviate all those aspects once theye have the descriptive parameteres they feel comfortable with the description not with the measures.

Finally, what it happens is that the test characteristic curve may differ very low between 3PL and rasch curves, due to the mathematical fact that it adds monotonic logistic curves, but again, the interpretation is not the same due to invariance of measure from both models.

Thank you Svend when you say: "why bother about the difference anyway?"

Regards
Agustin

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________________________________
From: Svend Kreiner <svkr at sund.ku.dk>
To: "rasch at acer.edu.au" <rasch at acer.edu.au>
Sent: Sunday, September 15, 2013 2:43 AM
Subject: Re: [Rasch] Comparison Rasch 3-parm IRT

It goes witout saying (almost) that 3pl estimates and Rasch estimates are "equivalent" if items actually fit the Rasch model except that we expect 3pl estmates to have a little larger standard errors than Rasch estmate, because th 3pl estmates use some of the available information in data to estimate two extra parameter per item.

If items do not fit the Rasch model, the two sets of estimates can not be expected to be equivalent. We may be able to find examples where they are similar, but also examples where they are not. But, given that items do not fit the Rasch model, you should not use Rasch estimates anyway, so why bother about the difference anyway.

Cheers Svend
________________________________________
From: rasch-bounces at acer.edu.au [rasch-bounces at acer.edu.au] on behalf of Mike Linacre [mike at winsteps.com]
Sent: Sunday, September 15, 2013 12:32 AM
To: rasch at acer.edu.au
Subject: Re: [Rasch] Comparison Rasch 3-parm IRT

Yes, Ricardo.

Ben Wright reached the same conclusion in his reanalysis of a major
dataset: "3PL ability estimates and item difficulties are statistically
equivalent to Rasch measures." - http://www.rasch.org/rmt/rmt91b.htm

Mike L.

On 9/14/2013 5:20 AM, Ricardo Primi wrote:
> Thanks a lot Mike
> It is interesting that then both models will tell the same history about the subjects (practically the same theta estimates and same S.E.)
> Thanks
>
> Ricardo

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