The Logistic Model and Estimation of Latent Structure

Abstract Consider the logistic model for dichotomous response involving a group of individuals with varying levels of ability and a set of items with varying degrees of difficulty. This article is concerned with estimating the parameters of the latent ability distribution for any given group of individuals. An iterative procedure for obtaining maximum likelihood estimates of these parameters based on the missing information principle is presented and illustrated with real data. The article also contains results on asymptotic variances and covariances of estimators and a discussion of the use of ability distributions in comparing groups of individuals. Key Words: Item analysisLogistic modelLatent structure estimationMissing information principleMaximum likelihood methodAbility distribution