7: Item Response Theory

Item response theory (IRT) refers to a theoretical and statistical framework for determining the likelihood of an item response in terms of examinee and item characteristics. The aim of IRT is to obtain estimates of (a) individuals’ standing (ability) on the unobserved latent trait (e.g., anxiety, mathematics ability), and (b) parameters characterizing the item (e.g., difficulty, discrimination). Within the framework of IRT, we can posit that a student’s probability of obtaining a correct response on a dichotomously scored multiple-choice achievement test item is based on ability and item characteristics. For example, one commonly used IRT model is the three-parameter logistic model that expresses the probability of a correct item response in terms of the examinee ability and three item characteristics. The person parameter is the trait estimate (e.g., reading ability) and is referred to as theta (θ). Item characteristics used to predict an examinee’s propensity to select a particular response option include: discrimination (a parameter), difficulty (b parameter), and the pseudo-guessing parameter (c parameter). Alternative IRT models can be applied to test data depending on the level of measurement of the item-level data and the number of traits believed to be measured by the items. The construct itself is a latent variable that is measured by the set of items, which serve the role of indicators much as did the observed variables in the factor analysis models described in Chapter 5 of this book. See Bock and Gibbons (2010), Bolt (2005), Lord and Novick (1968), Muthén and Lehman (1985), and, Thissen, Steinberg, and Wainer (1993) for a discussion on the relation between IRT and factor analysis parameters.