ON THE SAMPLING THEORY FOUNDATIONS OF ITEM RESPONSE THEORY MODELS

Item response theory (IRT) models are now in common use for the analysis of dichotomous item responses. This paper examines the sampling theory foundations for statistical inference in these models. The discussion includes: some history on the "stochastic subject" versus the random sampling interpretations of the probability in IRT models; the relationship between three versions of maximum likelihood estimation for IRT models; estimating theta-versus estimating theta-predictors; IRT models and loglinear models; the identifiability of IRT models; and the role of robustness and Bayesian statistics from the sampling theory perspective.