Inferring the Number of Attributes for the Exploratory DINA Model

Yinghan Chen (), Ying Liu (), Steven Andrew Culpepper () and Yuguo Chen ()
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Yinghan Chen: University of Nevada, Reno
Ying Liu: University of Illinois at Urbana-Champaign
Steven Andrew Culpepper: University of Illinois at Urbana-Champaign
Yuguo Chen: University of Illinois at Urbana-Champaign

Psychometrika, 2021, vol. 86, issue 1, No 2, 30-64

Abstract: Abstract Diagnostic classification models (DCMs) are widely used for providing fine-grained classification of a multidimensional collection of discrete attributes. The application of DCMs requires the specification of the latent structure in what is known as the $${\varvec{Q}}$$ Q matrix. Expert-specified $${\varvec{Q}}$$ Q matrices might be biased and result in incorrect diagnostic classifications, so a critical issue is developing methods to estimate $${\varvec{Q}}$$ Q in order to infer the relationship between latent attributes and items. Existing exploratory methods for estimating $${\varvec{Q}}$$ Q must pre-specify the number of attributes, K. We present a Bayesian framework to jointly infer the number of attributes K and the elements of $${\varvec{Q}}$$ Q . We propose the crimp sampling algorithm to transit between different dimensions of K and estimate the underlying $${\varvec{Q}}$$ Q and model parameters while enforcing model identifiability constraints. We also adapt the Indian buffet process and reversible-jump Markov chain Monte Carlo methods to estimate $${\varvec{Q}}$$ Q . We report evidence that the crimp sampler performs the best among the three methods. We apply the developed methodology to two data sets and discuss the implications of the findings for future research.

Keywords: diagnostic models; dimensionality; Dirichlet processes; Indian buffet process; reversible jump MCMC; Bayesian (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s11336-021-09750-9

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