Semi-Parametric Item Response Theory With O'Sullivan Splines for Item Responses and Response Time

Response time (RT) has been an essential resource for supplementing the estimation accuracy of latent traits and item parameters in educational testing. Most item response theory (IRT) approaches are based on parametric RT models. However, since test takers may alter their behaviors during a test due to motivation or strategy shifts, fatigue, or other causes, parametric IRT models are unlikely to capture such subtle and nonlinear information. In this work, we propose a novel semi-parametric IRT model with O'Sullivan splines to accommodate the flexible mean RT shapes and explore the underlying nonlinear relationships between latent traits and RT. A simulation study was conducted to demonstrate the substantial improvement in parameter estimation achieved by the new model, as well as the detriment of using parametric models in terms of biases and measurement errors. Using this model, a dataset of mathematics test scores and RT from the Programme for International Student Assessment was analyzed to demonstrate the evident nonlinearity and to compare the proposed model with existing models in terms of model fitting. The findings presented in this study indicate the promising nature of the new approach, suggesting its potential as an additional psychometric tool to enhance test reliability and reduce measurement errors.