IRT modeling doesn't care much whether an item is free response or not, just the scale on which it's scored. Binary and polytomous scoring = IRT model. Continuo

IRT modeling doesn't care much whether an item is free response or not, just the scale on which it's scored. Binary and polytomous scoring = IRT model. Continuous scoring = Factor analysis. If by mentioning free response, you mean students are unlikely to guess the correct answer, even when they don't know it, it's a 2 parameter IRT rather than 3. Best of luck! :)