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A Nonparametric Multidimensional Latent Class IRT Model in a Bayesian Framework

Author

Listed:
  • Francesco Bartolucci

    (Università di Perugia)

  • Alessio Farcomeni

    (Sapienza - Università di Roma)

  • Luisa Scaccia

    (Università di Macerata)

Abstract

We propose a nonparametric item response theory model for dichotomously-scored items in a Bayesian framework. The model is based on a latent class (LC) formulation, and it is multidimensional, with dimensions corresponding to a partition of the items in homogenous groups that are specified on the basis of inequality constraints among the conditional success probabilities given the latent class. Moreover, an innovative system of prior distributions is proposed following the encompassing approach, in which the largest model is the unconstrained LC model. A reversible-jump type algorithm is described for sampling from the joint posterior distribution of the model parameters of the encompassing model. By suitably post-processing its output, we then make inference on the number of dimensions (i.e., number of groups of items measuring the same latent trait) and we cluster items according to the dimensions when unidimensionality is violated. The approach is illustrated by two examples on simulated data and two applications based on educational and quality-of-life data.

Suggested Citation

  • Francesco Bartolucci & Alessio Farcomeni & Luisa Scaccia, 2017. "A Nonparametric Multidimensional Latent Class IRT Model in a Bayesian Framework," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 952-978, December.
    • Handle: RePEc:spr:psycho:v:82:y:2017:i:4:d:10.1007_s11336-017-9576-7
    DOI: 10.1007/s11336-017-9576-7
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    References listed on IDEAS

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    1. M. Onna, 2002. "Bayesian estimation and model selection in ordered latent class models for polytomous items," Psychometrika, Springer;The Psychometric Society, vol. 67(4), pages 519-538, December.
    2. 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.
    3. Irene Klugkist & Bernet Kato & Herbert Hoijtink, 2005. "Bayesian model selection using encompassing priors," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(1), pages 57-69, February.
    4. Bartolucci, Francesco & Scaccia, Luisa & Farcomeni, Alessio, 2012. "Bayesian inference through encompassing priors and importance sampling for a class of marginal models for categorical data," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4067-4080.
    5. Karl Christensen & Jakob Bjorner & Svend Kreiner & Jørgen Petersen, 2002. "Testing unidimensionality in polytomous Rasch models," Psychometrika, Springer;The Psychometric Society, vol. 67(4), pages 563-574, December.
    6. Bartolucci, Francesco & Bacci, Silvia & Gnaldi, Michela, 2014. "MultiLCIRT: An R package for multidimensional latent class item response models," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 971-985.
    7. Herbert Hojtink & Ivo Molenaar, 1997. "A multidimensional item response model: Constrained latent class analysis using the gibbs sampler and posterior predictive checks," Psychometrika, Springer;The Psychometric Society, vol. 62(2), pages 171-189, June.
    8. Jia-Chiun Pan & Guan-Hua Huang, 2014. "Bayesian Inferences of Latent Class Models with an Unknown Number of Classes," Psychometrika, Springer;The Psychometric Society, vol. 79(4), pages 621-646, October.
    9. Francesco Bartolucci, 2007. "A class of multidimensional IRT models for testing unidimensionality and clustering items," Psychometrika, Springer;The Psychometric Society, vol. 72(2), pages 141-157, June.
    10. Francesco Bartolucci & Antonio Forcina, 2005. "Likelihood inference on the underlying structure of IRT models," Psychometrika, Springer;The Psychometric Society, vol. 70(1), pages 31-43, March.
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    Cited by:

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    2. Francesco Dotto & Alessio Farcomeni & Maria Grazia Pittau & Roberto Zelli, 2019. "A dynamic inhomogeneous latent state model for measuring material deprivation," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 182(2), pages 495-516, February.

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