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

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  • Yan Huo
  • Jimmy de la Torre
  • Eun-Young Mun
  • Su-Young Kim
  • Anne Ray
  • Yang Jiao
  • Helene White

Abstract

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. Copyright The Psychometric Society 2015

Suggested Citation

  • Yan Huo & Jimmy de la Torre & Eun-Young Mun & Su-Young Kim & Anne Ray & Yang Jiao & Helene White, 2015. "A Hierarchical Multi-Unidimensional IRT Approach for Analyzing Sparse, Multi-Group Data for Integrative Data Analysis," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 834-855, September.
    • Handle: RePEc:spr:psycho:v:80:y:2015:i:3:p:834-855
    DOI: 10.1007/s11336-014-9420-2
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    References listed on IDEAS

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    1. Neal Thomas, 2002. "The role of secondary covariates when estimating latent trait population distributions," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 33-48, March.
    2. Jean-Paul Fox & Cees Glas, 2001. "Bayesian estimation of a multilevel IRT model using gibbs sampling," Psychometrika, Springer;The Psychometric Society, vol. 66(2), pages 271-288, June.
    3. A. Béguin & C. Glas, 2001. "MCMC estimation and some model-fit analysis of multidimensional IRT models," Psychometrika, Springer;The Psychometric Society, vol. 66(4), pages 541-561, December.
    4. Robert Mislevy, 1991. "Randomization-based inference about latent variables from complex samples," Psychometrika, Springer;The Psychometric Society, vol. 56(2), pages 177-196, June.
    5. Chalmers, R. Philip, 2012. "mirt: A Multidimensional Item Response Theory Package for the R Environment," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i06).
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    Cited by:

    1. Paul A. Jewsbury & Peter W. van Rijn, 2020. "IRT and MIRT Models for Item Parameter Estimation With Multidimensional Multistage Tests," Journal of Educational and Behavioral Statistics, , vol. 45(4), pages 383-402, August.

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