Semiparametric Estimation in the Rasch Model and Related Exponential Response Models, Including a Simple Latent Class Model for Item Analysis
本文揭示了Rasch模型中条件似然与混合模型方法的深层联系，证明当潜类数足够多时有限混合模型可给出与条件似然相同的项目参数估计，并提出了基于潜类技术的灵活项目分析方法。
Abstract The Rasch model for item analysis is an important member of the class of exponential response models in which the number of nuisance parameters increases with the number of subjects, leading to the failure of the usual likelihood methodology. Both conditional-likelihood methods and mixture-model techniques have been used to circumvent these problems. In this article, we show that these seemingly unrelated analyses are in fact closely linked to each other, despite dramatic structural differences between the classes of models implied by each approach. We show that the finite-mixture model for J dichotomous items having T latent classes gives the same estimates of item parameters as conditional likelihood on a set whose probability approaches one if T ≥ (J + 1)/2. Unconditional maximum likelihood estimators for the finite-mixture model can be viewed as Keifer-Wolfowitz estimators for the random-effects version of the Rasch model. Latent-class versions of the model are especially attractive when T is small relative to J. We analyze several sets of data, propose simple diagnostic checks, and discuss procedures for assigning scores to subjects based on posterior means. A flexible and general methodology for item analysis based on latent class techniques is proposed.