On Bayesian estimation of a latent trait model defined by a rank-based likelihood

Maximum likelihood estimation (frequentist) and Bayesian estimation are two common parameter estimation methods. However, maximum likelihood estimation faces limitations, including the effect of outliers, computational complexity, and issues with ordinal categorical data, leading to biased estimates and inaccurate coverage probabilities. To address these limitations, this study employed a latent trait model with a Bayesian marginal likelihood of rank-based estimation for parameter estimation. The simulation results demonstrated favorable performance of the proposed method. Trace plots of all parameters showed good distribution and quick convergence, with the potential scale reduction factor not exceeding 1, indicating no convergence issues. Furthermore, the posterior predictive check showed the simulated data closely resembled the observed data, indicating the method effectively captures within-region variation through a latent trait parameter. Performance metrics like mean absolute error, root mean square error, and 95% confidence interval coverage probability revealed the estimates from the proposed Bayesian method surpassed those from classical approaches. In conclusion, a latent traits model with Bayesian marginal likelihood and rank-based estimation is considered a superior parameter estimation technique compared to classical methods, particularly for dealing with ordinal categorical data.