A Hierarchical Multi-Unidimensional IRT Approach for Analyzing Sparse, Multi-Group Data for Integrative Data Analysis

Yan Huo, Jimmy de la Torre, Eun Young Mun, Su Young Kim, Anne E. Ray, Yang Jiao, Helene R. White

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


The present paper proposes a hierarchical, multi-unidimensional two-parameter logistic item response theory (2PL-MUIRT) model extended for a large number of groups. The proposed model was motivated by a large-scale integrative data analysis (IDA) study which combined data (N = 24,336) from 24 independent alcohol intervention studies. IDA projects face unique challenges that are different from those encountered in individual studies, such as the need to establish a common scoring metric across studies and to handle missingness in the pooled data. To address these challenges, we developed a Markov chain Monte Carlo (MCMC) algorithm for a hierarchical 2PL-MUIRT model for multiple groups in which not only were the item parameters and latent traits estimated, but the means and covariance structures for multiple dimensions were also estimated across different groups. Compared to a few existing MCMC algorithms for multidimensional IRT models that constrain the item parameters to facilitate estimation of the covariance matrix, we adapted an MCMC algorithm so that we could directly estimate the correlation matrix for the anchor group without any constraints on the item parameters. The feasibility of the MCMC algorithm and the validity of the basic calibration procedure were examined using a simulation study. Results showed that model parameters could be adequately recovered, and estimated latent trait scores closely approximated true latent trait scores. The algorithm was then applied to analyze real data (69 items across 20 studies for 22,608 participants). The posterior predictive model check showed that the model fit all items well, and the correlations between the MCMC scores and original scores were overall quite high. An additional simulation study demonstrated robustness of the MCMC procedures in the context of the high proportion of missingness in data. The Bayesian hierarchical IRT model using the MCMC algorithms developed in the current study has the potential to be widely implemented for IDA studies or multi-site studies, and can be further refined to meet more complicated needs in applied research.

Original languageEnglish
Pages (from-to)834-855
Number of pages22
Issue number3
StatePublished - 4 Sep 2015

Bibliographical note

Funding Information:
We would like to thank the following investigators who generously contributed their data to Project INTEGRATE: John S. Baer, Department of Psychology, The University of Washington, and Veterans’ Affairs Puget Sound Health Care System; Nancy P. Barnett, Center for Alcohol and Addiction Studies, Brown University; M. Dolores Cimini, University Counseling Center, The University at Albany, State University of New York; William R. Corbin, Department of Psychology, Arizona State University; Kim Fromme, Department of Psychology, The University of Texas, Austin; Joseph W. LaBrie, Department of Psychology, Loyola Marymount University; Mary E. Larimer, Department of Psychiatry and Behavioral Sciences, The University of Washington; Matthew P. Martens, Department of Educational, School, and Counseling Psychology, The University of Missouri; James G. Murphy, Department of Psychology, The University of Memphis; Scott T. Walters, Department of Behavioral and Community Health, The University of North Texas Health Science Center; Helene R. White, Center of Alcohol Studies, Rutgers, The State University of New Jersey; and Mark D. Wood, Department of Psychology, The University of Rhode Island. The project described was supported by Award Number R01 AA019511 from the National Institute on Alcohol Abuse and Alcoholism (NIAAA). The content is solely the responsibility of the authors and does not necessarily represent the official views of the NIAAA or the National Institutes of Health.

Publisher Copyright:
© 2014, The Psychometric Society.


  • IDA
  • IRT
  • MCMC
  • multi-unidimensional
  • multiple groups


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