Gibbs-Slice Sampling Algorithm for Estimating the Four-Parameter Logistic Model - Zhang, Jiwei; Lu, Jing; Du, Hang; Zhang, Zhaoyuan (Frontiers in Psychology, 2020)
The four-parameter logistic (4PL) model has recently attracted much interest in educational testing and psychological measurement. This paper develops a new Gibbs-slice algorithm for estimating the 4PL model parameters in the framework of a fully Bayesian. Here, Gibbs algorithm is employed to improve the sampling efficiency by using the conjugate prior distributions in updating asymptote parameters. Slice algorithm is used to update 2PL model parameters, which overcomes the dependence of Metropolis Hastings algorithm on the proposal distribution (tuning parameters). In fact, Gibbs-slice algorithm not only improves the accuracy of parameter estimation but also enhances sampling efficiency. Simulation studies are conducted to show the good performance of the proposed Gibbs-slice algorithm and to investigate the impact of the different prior distributions on the accuracy of parameter estimation. Based on the Markov Chain Monte carlo samples from the posterior distributions, the deviance information criterion and the logarithm of the pseudomarignal likelihood are considered to assess the model fittings. Moreover, a detailed analysis of the PISA data is carried out to illustrate the proposed methodology.