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 [Formula: see text] matrix. Expert-specified [Formula: see text] matrices might be biased and result in incorrect diagnostic classifications, so a critical issue is developing methods to estimate [Formula: see text] in order to infer the relationship between latent attributes and items. Existing exploratory methods for estimating [Formula: see text] 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 [Formula: see text]. We propose the crimp sampling algorithm to transit between different dimensions of K and estimate the underlying [Formula: see text] 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 [Formula: see text]. 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: Bayesian; Dirichlet processes; Indian buffet process; diagnostic models; dimensionality; reversible jump MCMC.