Multilevel higher-order item response theory models

Hung-Yu HUANG, Wen Chung WANG

Research output: Contribution to journalArticlespeer-review

9 Citations (Scopus)


In the social sciences, latent traits often have a hierarchical structure, and data can be sampled from multiple levels. Both hierarchical latent traits and multilevel data can occur simultaneously. In this study, we developed a general class of item response theory models to accommodate both hierarchical latent traits and multilevel data. The freeware WinBUGS was used for parameter estimation. A series of simulations were conducted to evaluate the parameter recovery and the consequence of ignoring the multilevel structure. The results indicated that the parameters were recovered fairly well; ignoring multilevel structures led to poor parameter estimation, overestimation of test reliability for the second-order latent trait, and underestimation of test reliability for the first-order latent traits. The Bayesian deviance information criterion and posterior predictive model checking were helpful for model comparison and model-data fit assessment. Two empirical examples that involve an ability test and a teaching effectiveness assessment are provided. Copyright © 2013 The Author(s).
Original languageEnglish
Pages (from-to)495-515
JournalEducational and Psychological Measurement
Issue number3
Early online dateNov 2013
Publication statusPublished - 2014


Huang, H.-Y., & Wang, W.-C. (2014). Multilevel higher-order item response theory models. Educational and Psychological Measurement, 74(3), 495–515.


  • Item response theory
  • Higher-order latent trait
  • Multilevel model
  • Markov chain Monte Carlo (MCMC) estimation


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