A Gibbs sampler for the multidimensional four‐parameter logistic item response model via a data augmentation scheme

Zhihui Fu, Susu Zhang, Ya‐hui Su, Ningzhong Shi, Jian Tao

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)427-464
Number of pages38
JournalBritish Journal of Mathematical and Statistical Psychology
Volume74
Issue number3
DOIs
StatePublished - Nov 2021

Keywords

  • Bayes estimation
  • data augmentation
  • deviance information criterion
  • Gibbs sampling
  • multidimensional four-parameter logistic item response theory model

ASJC Scopus subject areas

  • Psychology(all)
  • Arts and Humanities (miscellaneous)
  • Statistics and Probability

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