Expected Response Functions

Abstract

Item response theory makes use of what are sometimes referred to as item response functions. Such a function is actually a probability density function (pdf) for the response of an individual to a test item, given the values of certain parameters, classified as item parameters and person parameters (or abilities). In testing, there is typically a calibration phase, in which item parameters are estimated and abilities are ignored. This is followed by an application phase, in which abilities are estimated while conditioning on the estimated values of the item parameters. A Bayesian alternative to treating the item parameters as known quantities involves replacing item response functions with another class of pdfs, referred to as expected response functions (ERFs). The latter take the uncertainty regarding item parameters into account for purposes of estimating abilities. This chapter provides a formal description of ERFs and briefly illustrates their application to the Rasch model for binary item responses.