# Estimating IRT item parameters when ability and response are know

I have 500,000 students dichotomy responses for a 45 item test. I know the ability of the this students, that this ability was calculated from this responses using 3PL model by Expected a Posteriori (EAP) and I know the prior mean and standard deviation used. Having this information it's possible in R to know or at least get a approximation of the 3 parameters of each items that were used to calculated the students ability?

I am not interested in recalculating the value of the parameters, but rather to know the values of the parameters used by those who prepared the test.

I don't think there is an easy way to calculate them. You can only estimate them. Assuming that the $$\theta$$ is known, you can write a function to optimize the loglikelihood function for a given response vector of each item.