IRT parameter estimation with Bayesian MCMC methods for small samples in Islamic schools

This study aims to estimate item parameters in Item Response Theory (IRT) using the Bayesian Markov Chain Monte Carlo (MCMC) method in the context of Islamic schools in Pekalongan Regency/City, where small sample sizes pose a challenge. Unlike conventional methods such as maximum likelihood estimation, which tend to yield biased results with limited data, Bayesian MCMC incorporates prior knowledge and contextual information to improve estimation accuracy. Simulated datasets with varying sample sizes (30, 100, 300, 1000) and item numbers (10, 25, 30, 40) were used to compare the performance of Bayesian MCMC with traditional IRT methods. The results show that Bayesian MCMC produces more stable and accurate estimates, particularly in small-sample conditions. These findings suggest that Bayesian approaches are effective for psychometric analysis in Islamic education settings. The study concludes that Bayesian MCMC is a valuable method for improving the robustness of item parameter estimation in limited-data contexts.