Evaluating model assumptions in item response theory

Abstract

This dissertation deals with the evaluation of model assumptions in the context of item response theory. Item response theory, also known as modern test theory, provides a statistical framework for the measurement of psychological constructs that cannot by observed directly, such as intelligence or depression. Item response theory models attempt to measure these psychological constructs by relating these 'latent traits' to observed responses on a set of items that are designed to measure these constructs (e.g., an intelligence test). For these item response theory models to be valid, the assumptions defining these models have to be valid. This dissertation deals with the issue of evaluating the model assumptions in item response theory. Two model assumptions are considered in particular: latent monotonicity and invariant item ordering. Observable consequences of these assumptions are presented and statistical tests are proposed that evaluate these observable consequences. Using these statistical procedures, it is possible to evaluate these model assumptions. The application of these procedures is illustrated using empirical data.