Kernel Smoothing Item Response Theory in R: A Didactic

Abstract

Item response theory (IRT) refers to a family of mathematical models which describe the relationship between latent continuous variables (unobserved attribute or characteristic) and their manifestations (dichotomous/polytomous observed outcomes or responses) with regard to a set of item characteristics. Researchers typically use parametric IRT (PIRT) models to measure educational and psychological latent variables. However, PIRT models are based on a set of strong assumptions that often are not satisfied. For this reason, non-parametric IRT (NIRT) models can be more desirable. An exploratory NIRT approach is kernel smoothing IRT (KS-IRT; Ramsay, 1991) which estimates option characteristic curves by non-parametric kernel smoothing technique. This approach only gives graphical representations of item characteristics in a measure and provides preliminary feedback about the performance of items and measures. Although KS-IRT is not a new approach, its application is far from widespread, and it has limited applications in psychological and educational testing. The purpose of the present paper is to give a reader-friendly introduction to the KS-IRT, and then use the KernSmoothIRT package (Mazza et al., 2014, 2022) in R to straightforwardly demonstrate the application of the approach using data of Children’s Test Anxiety scale.