Multidimensional Bayesian adaptive testing

This paper introduces a fully Bayesian approach to multidimensional adaptive testing (MBAT). By incorporating uncertainty in both item and person parameter estimates, MBAT addresses limitations in conventional multidimensional adaptive testing (MAT), which relies on point item and person parameter estimates. A Monte Carlo simulation was conducted to evaluate the performance of MBAT compared to conventional MAT. The study was based on a four-factorial design, with the factors calibration sample size (N = 250, N = 500, N = 1,000), test length (t = 30, t = 60), true trait level (- 2.0, - 1.5, …, 2.0), and MAT algorithm (MAT, MBAT), across a three-dimensional trait structure with within- and between-item multidimensionality. The results showed that MBAT consistently outperformed conventional MAT in terms of the bias and mean squared error (MSE) of the final person parameter estimates, especially at the extremes of the trait distributions. Implemented in general-purpose software (Stan, R), the approach is computationally feasible and adaptable, providing a practical foundation for future research and applications in MAT.