I'd say just logistic regression. It's a 1PL IRT model (though a Rasch purist would hate me for saying this). Basically it answers the question "Given your ability level what is the probability you'll answer this item correctly?" I learned about IRT models but not a lot about Rasch. Some say the IRT 1PL is the same as the Rasch but as I already stated a Rasch purist would argue differently. That's really all I know about Rasch models.

Spunky is a psychometrics person so hopefully he sees this and provides more insight.