A Gibbs sampler for the multidimensional four‐parameter logistic item response model via a data augmentation scheme. (18th May 2021)

• Record Type: Journal Article
• Authors: Fu, Zhihui; Zhang, Susu; Su, Ya‐Hui; Shi, Ningzhong; Tao, Jian
• Is Part Of: British journal of mathematical & statistical psychology. Volume 74:Part 3(2021)
• Page Start: 427
• Page End: 464
• Publication Date: 2021-05-18
• Subjects: Bayes estimation -- data augmentation -- Gibbs sampling -- multidimensional four‐parameter logistic item response theory model -- deviance information criterion; Psychometrics -- Periodicals; Psychology -- Mathematical models -- Periodicals; Psychology -- Statistical methods -- Periodicals; 150.727
• DOI: 10.1111/bmsp.12234
• Languages: English
• ISSNs: 0007-1102

Abstract

Abstract : The four‐parameter logistic (4PL) item response model, which includes an upper asymptote for the correct response probability, has drawn increasing interest due to its suitability for many practical scenarios. This paper proposes a new Gibbs sampling algorithm for estimation of the multidimensional 4PL model based on an efficient data augmentation scheme (DAGS). With the introduction of three continuous latent variables, the full conditional distributions are tractable, allowing easy implementation of a Gibbs sampler. Simulation studies are conducted to evaluate the proposed method and several popular alternatives. An empirical data set was analysed using the 4PL model to show its improved performance over the three‐parameter and two‐parameter logistic models. The proposed estimation scheme is easily accessible to practitioners through the open‐source IRTlogit package.