ABSTRACT
The purpose of this chapter is to present an EM algorithm, which carries out fully semiparametric estimation for the two-parameter latent trait model. The approach is based on the theory of nonparametric estimation of mixtures. The original research in this area was initiated by Kiefer and Wolfowitz, who proved that the maximum likelihood (ML) estimator of a structural parameter is strongly consistent, when the incidental parameters are independently distributed random variables with a common unknown distribution F. Lindsay studied the geometry of the likelihood of the estimator of a mixture density and gave conditions on the existence, discreteness, support size characterisation and uniqueness of the estimator. His results are based on the directional derivative of the loghkelihood towards a support point, and this used in this chapter to discover the ideal amount points needed to about the earlier for the latent trait model.
