A Two-Parameter IRT Model With Ability-Based Guessing: Estimation Using the Stochastic EM Algorithm

In this paper, we propose a two-parameter normal ogive model with ability-based guessing (2PNO-AG), which extends the one-parameter logistic AG (1PL-AG) model by allowing item discrimination parameters to vary across items. To facilitate parameter estimation, we develop a stochastic expectation-maximization (StEM) algorithm tailored to the 2PNO-AG structure. The performance of the proposed model and estimation algorithm is evaluated through both simulation studies and empirical data analysis. The simulation results demonstrate that (a) the StEM algorithm yields accurate and stable parameter estimates under a range of initial values and prior specifications, and (b) the 2PNO-AG model offers greater robustness and flexibility compared to the 1PL-AG and three-parameter normal ogive models. Furthermore, an empirical analysis using data from 664 German fourth-grade students, obtained from the item response warehouse, confirms the superiority of the 2PNO-AG model, showing a significantly better model fit than competing alternatives.