Mixture‐modelling‐based Bayesian MH‐RM algorithm for the multidimensional 4PLM

Abstract

Several recent works have tackled the estimation issue for the unidimensional four‐parameter logistic model (4PLM). Despite these efforts, the issue remains a challenge for the multidimensional 4PLM (M4PLM). Fu et al. (2021) proposed a Gibbs sampler for the M4PLM, but it is time‐consuming. In this paper, a mixture‐modelling‐based Bayesian MH‐RM (MM‐MH‐RM) algorithm is proposed for the M4PLM to obtain the maximum a posteriori (MAP) estimates. In a comparison of the MM‐MH‐RM algorithm to the original MH‐RM algorithm, two simulation studies and an empirical example demonstrated that the MM‐MH‐RM algorithm possessed the benefits of the mixture‐modelling approach and could produce more robust estimates with guaranteed convergence rates and fast computation. The MATLAB codes for the MM‐MH‐RM algorithm are available in the online appendix.