The semi-parametric Cox proportional hazards latent trait model provides flexibility in fitting response times without imposing strong assumptions like parametric models, but it brings estimation challenges. In this paper, we propose a flexible and efficient slice sampling algorithm within a fully Bayesian framework to estimate the hierarchical piecewise constant proportional hazards latent trait model. A comprehensive evaluation of this new Bayesian method is conducted through multiple simulation studies, considering various factors such as different sample sizes, diverse types of prior distributions, and varying strengths of speed and ability correlations. The proposed algorithm was also compared with the adaptive rejection for Gibbs sampling algorithm in a simulation study. In addition, four Bayesian model evaluation criteria are presented to assess model fit. The proposed parameter estimation technique is further exemplified using the computer-based Program for International Student Assessment science data.
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