Equal Area Estimation of Three-Parameter Logistic Model for Item Response Theory

Item response theory (IRT) is used commonly for design of tests, test assembly, test scaling and calibration, construction of test item banks, investigations of test item bias, and other common procedures in the test development process. Logistic function is the most popular unidimensional IRT model. Applications of IRT models require obtaining the set of values for logistic function parameters that best fit an empirical data set. However, success in obtaining such set of values does not guarantee that the constructs they represent actually exist, for the adequacy of a model is not sustained by the possibility of estimating parameters. In this study, an Equal ARea Logistic estimation algorithm (EARL) is proposed. The EARL algorithm can estimate the parameters, which are discrimination, difficulty and pseudo-guessing level, of the logistic model. Numerical results of two-parameter and three-parameter estimation are presented to show the stability, accuracy and time-saving of the algorithm.