Parameter estimation in latent trait models

Latent trait models for binary responses to a set of test items are considered from the point of view of estimating latent trait parametersθ=(θ1, …,θn) and item parametersβ=(β1, …,βk), whereβj may be vector valued. Withθ considered a random sample from a prior distribution with parameterφ, the estimation of (θ, β) is studied under the theory of the EM algorithm. An example and computational details are presented for the Rasch model.