The No-U-Turn sampler and its mixture-modeling revision for the 4-parameter normal ogive model

Introduction: The No-U-Turn Sampler (NUTS), widely applied in psychometrics via the Stan platform, lacks algorithm-level systematic introduction for item response theory (IRT) models and tailored optimizations for specific models. This study systematically explicates the NUTS algorithm for the 4-parameter normal ogive (4PNO) model and proposes a Mixture-Modeling NUT sampler (MMNUTS) to enhance its estimation. Methods: A simulation study that considers both educational and psychological scenarios with an empirical example from a behavioral scale was designed to examine the feasibility of the proposed MMNUTS. A recoverability comparison is performed among the NUT sampler in Stan, MMNUTS, and the Gibbs-within-Gibbs sampler in the R package fourPNO. Results: All samplers achieved satisfactory convergence, with estimation accuracy improved at larger sample sizes. MMNUTS showed significant superiority in running time and upper asymptote parameter recovery in the psychological scenario with less informative priors and 5,000 samples. The 4PNO model yielded optimal fit in the empirical analysis, with MMNUTS demonstrating faster convergence and higher computational efficiency than the other two samplers. Discussion: The proposed MMNUTS maintains robust estimation accuracy while improving computational efficiency for the 4PNO model, providing a foundational reference for developing tailored sampling algorithms for complex psychometric models. The MATLAB codes for MMNUTS are presented in the appendix.