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 parameters θ = ( θ 1 , …, θ n ) and item parameters β =( β 1 , …, β k ), where β j may be vector valued. With θ considered a random sample from a prior distribution with parameter ϕ , 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.