b Parameter

Item response theory (IRT) uses several parameters. These parameters control the position and shape of IRT item characteristic curves (ICCs) that map the relationship between an examinee’s ability, usually denoted by theta (θ), and the examinee’s probability of making a particular item response (see Figure 1). The b parameter is present in all common IRT models. It is called the difficulty parameter, as it is the IRT analogy to traditional measures of item difficulty, such as p values. This entry first provides further context and discusses the importance of the b parameter. It then discusses unidimensional IRT models for dichotomous items and polytomous items, multidimensional IRT (MIRT) models, and the relationship between p values and IRT b parameters.