, Volume 82, Issue 4, pp 952–978 | Cite as

A Nonparametric Multidimensional Latent Class IRT Model in a Bayesian Framework

  • Francesco BartolucciEmail author
  • Alessio Farcomeni
  • Luisa Scaccia


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.


cluster analysis encompassing priors item response theory unidimensionality Markov chain Monte Carlo reversible-jump algorithm stochastic partitions 


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© The Psychometric Society 2017

Authors and Affiliations

  1. 1.Dipartimento di EconomiaUniversità di PerugiaPerugiaItaly
  2. 2.Dipartimento di Sanità Pubblica e Malattie InfettiveSapienza - Università di RomaRomeItaly
  3. 3.Dipartimento di Economia e DirittoUniversità di MacerataMacerataItaly

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