, Volume 62, Issue 2, pp 171–189 | Cite as

A multidimensional item response model: Constrained latent class analysis using the gibbs sampler and posterior predictive checks

  • Herbert Hojtink
  • Ivo W. Molenaar


In this paper it will be shown that a certain class of constrained latent class models may be interpreted as a special case of nonparametric multidimensional item response models. The parameters of this latent class model will be estimated using an application of the Gibbs sampler. It will be illustrated that the Gibbs sampler is an excellent tool if inequality constraints have to be taken into consideration when making inferences. Model fit will be investigated using posterior predictive checks. Checks for manifest monotonicity, the agreement between the observed and expected conditional association structure, marginal local homogeneity, and the number of latent classes will be presented.

Key words

Gibbs sampler posterior predictive checks nonparametric item response theory multidimensional manifest monotonicity local homogeneity conditional association 


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Copyright information

© The Psychometric Society 1997

Authors and Affiliations

  • Herbert Hojtink
    • 1
  • Ivo W. Molenaar
    • 1
  1. 1.Department of Statistics and Measurement TheoryUniversity of GroningenThe Netherlands

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