Slice sampling algorithm for estimating the item response theory model with ordinal response data

Abstract

In this paper, a highly effective slice sampling algorithm is proposed to estimate the graded response model that has been widely used in educational psychological assessments. The new algorithm not only avoids the Metroplis–Hastings algorithm boring adjustment the turning parameters to achieve an appropriate acceptance probability, but also overcomes the dependence of the traditional Gibbs sampling algorithm on the conjugate prior distribution. Three simulation studies are conducted and a detailed analysis of sexual compulsivity scale (SCS) data is carried out to further illustrate the proposed methodology.

Keywords:

• Bayesian estimation
• Item response theory
• Gibbs sampling algorithm
• Graded response model
• Metropolis–Hastings sampling algorithm
• Slice sampling algorithm

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (Grant No. 12001091), China Postdoctoral Science Foundations (Grant No. 2021M690587 and Grant No. 2021T140108), the Fundamental Research Funds for the Central Universities of China (Grant No. 2412020QD025).