Hi all,
I am working on a dissertation that analyzes some international tests of
mathematics achievement. I need to use the responses (which can be
considered "correct"/"incorrect") and estimate an IRT (Item Response Theory)
model to describe the test.
In a nutshell, assume the test measures a single trait in an individual.
Then the IRT curve that I am looking for (something they call a 3-parameter
logistic, which I think is not a 100% correct name) is described by the
following function (best viewed in a fixed-width font):
1 - c
P(T)= c + -------------------
-1.7 a(T - b)
1 + e
This curve takes a person's ability T and produces the probability that a
person with that trait will answer the question correctly.
The main problem, of course, is that T is unknown, as well as the three
parameters a, b, and c. So the estimation problem is quite tricky. I can't
find a reference that tells me exactly the recipe for finding it, but the
best I can tell is that the algorithm would start with an initial guess for
T, fit the curve parameters a, b, and c, then use this curve to re-estimate
T. The process repeats until some convergence criterion is reached.
Does anyone know if SAS will do this? I have found a piece of software that
claims to fit "Rasch models", but the classical Rasch model is a
one-parameter version of what I'm looking for (set b and c to zero, and you
have a Rasch model). Plus, the software costs about $1000, and I don't have
that to spare. The software (one called "BIGSTEPS" is the only one I can
find that will deal with the 89,000 students I have to deal with) is not
exactly "Microsoft Bob" in its ease of use.
This whole IRT/Rasch area is brand new to me, so I may be asking the wrong
crowd, but if anyone has any SAScode or guidance, I'd sure like to hear it.
--
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