Estimating Ability and Item Parameters

In its simplest form, the parameter estimation problem is the following. We are given a matrix U ≡ ∥u_ia ∥ consisting of the responses (u_ia = 0 or 1) of each of N examinees to each of n items. We assume that these responses arise from a certain model such as Eq. (2-1) or (2-2). We need to infer the parameters of the model: a_i , b_i , c_i (i = 1, 2, …, n) and θ _a (a = 1, 2,…, N).