If I have the item parameters for a set of polytomous questions, how can I mathematically convert a set of previous responses to ability scores? I have looked into different types of estimation methods, and from what I read EAP, MAP, and ML all perform similarly with higher amounts of items. I'm looking to create my own program to convert these old responses to ability scores based on the IRT analysis of these items I have done. So I have the item parameters for these specific items, as well as their responses, does anyone have a straightforward explanation of how these can be used in estimating theta?
My model doesn't include Rasch properties, so to get the initial item parameters, I used the Graded Response Model. Given that I have the original responses to the items, and the item parameters based on the GRM, what are the best ways to estimate theta from these?
Would it be more straightforward to do IRT for summed scores as explained in Thissen, Pommerich, Billeaud, & Williams (1995)?
Ha ha, yeah, I realized there's a lot behind what I was looking for. There are so many ways of estimating theta, and from what I've read so far, Weighted Likelihood Estimation or (a form of) Maximum Likelihood may be the route to go (Bayesian methods, like EAP and MAP, seem to be more biased at extremes of theta). But I was seeing if anyone out here knew of a good explanation of it and maybe an example of how theta is calculated using either of these methods. But I'll definitely check out that book, thanks so much for the recommendation!
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