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A Nonparametric Multidimensional Latent Class IRT Model in a Bayesian Framework

Published online by Cambridge University Press:  01 January 2025

Francesco Bartolucci Open the ORCID record for Francesco Bartolucci [Opens in a new window] ,
Alessio Farcomeni Open the ORCID record for Alessio Farcomeni [Opens in a new window]  and
Luisa Scaccia Open the ORCID record for Luisa Scaccia [Opens in a new window]
Francesco Bartolucci*
Affiliation:
Università di Perugia
Alessio Farcomeni
Affiliation:
Sapienza - Università di Roma
Luisa Scaccia
Affiliation:
Università di Macerata
*
Correspondence should be made to Francesco Bartolucci, Dipartimento di Economia, Università di Perugia, Via A. Pascoli 20, 06123, Perugia, Italy. Email: francesco.bartolucci@unipg.it
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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.

Keywords

cluster analysisencompassing priorsitem response theoryunidimensionalityMarkov chain Monte Carloreversible-jump algorithmstochastic partitions
Type
Original Paper
Information
Psychometrika , Volume 82 , Issue 4 , December 2017 , pp. 952 - 978
Copyright
Copyright © 2017 The Psychometric Society

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