Jean-Benoit Hardouin wrote:
>There is two a frequentist appoach which is the ONE Parameter Logistic
Model (OPLM) which is different of the 1-PLM(=Rasch model). The OPLM
allows defining a value of slope (discriminating power) different for
each item. The difference with the 2PLM is that this slopes are a priori
fixed by the user. The properties of the OPLM are very close of the
Rasch model (objective measure, exhaustivity of the score), with a
besser flexibility compare to the Rasch model. This is possible to
implement this model with gllamm>
Hmmm, so you fix the slope a priori. I'm not familiar with this model as
a "named" model but it begs the question of how you got the slope first.
>> Just to note this is an area of substantial dispute.
>Yes !!
The "heat" of the dispute seems to be dying down, finally.
>I don't hate the 2PLM but I don't see any advantage of this model
compared to the Rasch family model (which have nice measurement
properties) or compared to the Classical Test Theory (where the measure
generally is more reliable). I think the 2PLM is a pretty statistical
tool to verify the proposition "the model should have a good fit to the
data", but is not a very usefull model for a practical use (in the idea
to create a measure with good properties (psychometric point of view) or
reliable (practical point of view)).>
Whereas I think classical test theory is a crummy approximation to the
analysis you really wanted to do in the first place. I suspect much
depends on one's training---mine was from Rod McDonald, and thus I view
IRT as simply a special factor analysis for binary items that deals with
the nonlinear regression between latent trait and observed responses.
Unidimensional IRT isn't something particularly desirable.
>>If the Rasch model don't agree with another population than this one
used to check the fit, then there is Differential Item Functionning
which is well described in the literatture and which can be taking
account, even with the Rasch model !<<
Hmmm, DIF is not how I'd think about that problem.
My issue was to consider a set of data someone gave you. You want to
analyze it, let's say to screen for "good" items you plan on testing
again sometime later. In this case a 2PL type model (or even other
things like a nonparametric model) will be helpful.
This is best done with a good set of items to anchor things, though. So
if you have a set of items you understand, perhaps built according to
the Rasch model, it makes sense to use a 2PL (or restricted 2PL, or some
other) to analyze them to see if the new items perform similar to the
old items.
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