Bayesian Inference for IRT Models with Non-Normal Latent Trait Distributions

Xue Zhang, Chun Wang, David J. Weiss, Jian Tao

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Normality of latent traits is a common assumption made when estimating parameters for item response theory (IRT) models, but this assumption may be violated. The purpose of this research was to present a new Markov chain Monte Carlo (MCMC) method for ordinal items with flexible latent trait distributions (i.e., skewed and bimodal). Specifically, the Davidian curve (DC) was used to approximate the distribution of latent traits. The performance of the proposed MCMC algorithm with DCs was evaluated via a simulation study and compared with an EM method using DCs that is available in the “mirt” package (Chalmers, 2012). The manipulated factors included the number of response categories, sample size, and the shape of the latent trait distribution. The Hanna-Quinn (HQ) criterion was used to choose the best DC order. Results indicated that when informative priors were used, the MCMC algorithm with DCs could fit a flexible distribution well and the method provided good parameter estimates which, under some circumstances, had lower bias and RMSE than the EM method.

Original languageEnglish (US)
Pages (from-to)703-723
Number of pages21
JournalMultivariate Behavioral Research
Issue number5
Early online dateJun 29 2020
StatePublished - 2021

Bibliographical note

Funding Information:
Funding: This work was supported by Grant 2019M661194 from the Project funded by China Postdoctoral Science Foundation awarded to the first author. This research was also supported by the Eunice Kennedy Shriver National Institutes of Child Health and Human Development of the National Institutes of Health under Award Number R01HD079439 to the Mayo Clinic in Rochester Minnesota through a subcontract to the University of Minnesota and University of Washington, and IES R305D170042 award.

Publisher Copyright:
© 2020 Taylor & Francis Group, LLC.


  • Davidian curve
  • MCMC
  • flexible distribution
  • item response theory

PubMed: MeSH publication types

  • Journal Article


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