#9284. A Gibbs sampler for the multidimensional four-parameter logistic item response model via a data augmentation scheme

August 2026publication date
Proposal available till 29-05-2025
4 total number of authors per manuscript3510 $

The title of the journal is available only for the authors who have already paid for
Journal’s subject area:
Applied Mathematics;
Psychology (all);
Places in the authors’ list:
place 1place 2place 3place 4
FreeFreeFreeFree
1050 $940 $820 $700 $
Contract №9284.1 Contract №9284.2 Contract №9284.3 Contract №9284.4
1 place - free (for sale)
2 place - free (for sale)
3 place - free (for sale)
4 place - free (for sale)

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.
Keywords:
Bayes estimation; data augmentation; deviance information criterion; Gibbs sampling; multidimensional four-parameter logistic item response theory model

Contacts :
0