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 dimen- sions 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.

Bartolucci, F., Farcomeni, A., Scaccia, L. (2017). A nonparametric multidimensional latent class IRT Model in a Bayesian framework. PSYCHOMETRIKA, 82(4), 1-27 [10.1007/s11336-017-9576-7].

A nonparametric multidimensional latent class IRT Model in a Bayesian framework

Farcomeni, Alessio;
2017-01-01

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 dimen- sions 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.
2017
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore SECS-S/01 - STATISTICA
English
cluster analysis; encompassing priors; item response theory; markov chain monte carlo; reversible-jump algorithm; stochastic partitions; unidimensionality; psychology (all); applied mathematics
Bartolucci, F., Farcomeni, A., Scaccia, L. (2017). A nonparametric multidimensional latent class IRT Model in a Bayesian framework. PSYCHOMETRIKA, 82(4), 1-27 [10.1007/s11336-017-9576-7].
Bartolucci, F; Farcomeni, A; Scaccia, L
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/222177
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