Estimating Latent Distribution of Item Response Theory Using Kernel Density Method

The article proposes a new approach to estimating the latent distribution of item response theory (IRT) using kernel density estimation (KDE), particularly the solve-the-equation (STE) algorithm developed by Sheather and Jones (1991). As with existing methods, the KDE method aims to estimate the latent distribution of IRT to reduce biases in parameter estimates when the normality assumption on the latent variable is violated. Simulation studies and an empirical example confirm the robustness of algorithmic convergence of the KDE approach, and show that the KDE approach yields parameter estimates that are more accurate than or comparable to existing methods. Unlike other approaches that require multiple model fits for smoothing parameter selection, KDE requires only a single model-fitting step, substantially reducing computation time. These findings highlight KDE as a practical and efficient method for estimating latent distributions in IRT.