A. Introduction to IRTWhat is IRT?Item response theory relates characteristics of items (item parameters) and characteristics of individuals (latent traits) to the probability of a positive response. A variety of IRT models have been developed for dichotomous and polytomous data. In each case, the probability of answering correctly or endorsing a particular response category can be represented graphically by an item (option) response function (IRF/ORF). These functions represent the nonlinear regression of a response probability on a latent trait, such as conscientiousness or verbal ability (Hulin, Drasgow, & Parsons, 1983).Why is IRT useful?IRT provides several advantages over classical test theory (CTT) methods for constructing tests and examining measurement equivalence.Unlike CTT item statistics, which depend fundamentally on the subset of items and persons examined, IRT item and person parameters are invariant. This makes it possible to examine the contribution of items individually as they are added and removed from a test. Moreover, IRT allow researchers to calculate conditional standard errors of measurement based on a test information function, rather than assuming an average standard error across all trait levels as in CTT. This allows researchers to select items that provide maximum measurement precision in a particular ability/trait range (Hulin et al., 1983). Second, IRT allows researchers to conduct rigorous tests of measurement equivalence across experimental groups. This is particularly important in cross-cultural research where groups are expected to show mean differences on the attribute being measured. IRT methods can distinguish item bias from true differences on the attribute measured, whereas CTT methods cannot (Kim, Cohen, & Park, 1995). IRT also facilitates computer adaptive testing. Items can be selected that provide the most information for each examinee. This can dramatically reduce time and costs associated with test administration (Hulin et al., 1983). |