Factor Analysis and Latent Structure: IRT and Rasch Models

Abstract

Educational assessments, psychological scales, and social surveys often generate data in the form of a two-way array of discrete response data for N subjects (examinees, respondents, etc.) and J probes (test, scale, or survey items). Subjects' responses to the probes may be viewed as fallible measures of one or more underlying constructs, represented generically by a scalar or vector-valued index {latent variable} for each subject. When the response variables are discrete-valued, item response theory (IRT) and its variants provide a set of modeling and estimation tools for making inferences about the relationships between the Xij and the latent variable(s) θi and about subjects' location in the latent structure represented by θ. This article reviews standard parametric IRT models and estimation methods, extensions to compelx data analysis setting by way of a hierarchical Bayes formulation, nonparametric approaches to IRT, and selected applications in education, psychology, the social sciences, and biostatistics. Extensions of IRT to handle cognitively diagnostic assessment are briefly sketched, and similarities between IRT and Bayesian inference networks are pointed out.