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 \({\varvec{Q}}\) matrix. Expert-specified \({\varvec{Q}}\) matrices might be biased and result in incorrect diagnostic classifications, so a critical issue is developing methods to estimate \({\varvec{Q}}\) in order to infer the relationship between latent attributes and items. Existing exploratory methods for estimating \({\varvec{Q}}\) 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 \({\varvec{Q}}\). We propose the crimp sampling algorithm to transit between different dimensions of K and estimate the underlying \({\varvec{Q}}\) 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 \({\varvec{Q}}\). 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.

诊断分类模型 (DCM) 被广泛用于提供离散属性的多维集合的细粒度分类。DCM 的应用需要在所谓的\({\varvec{Q}}\)矩阵中指定潜在结构。专家指定的\({\varvec{Q}}\)矩阵可能有偏差并导致错误的诊断分类，因此一个关键问题是开发估计\({\varvec{Q}}\)的方法以推断潜在属性和项目之间的关系。用于估计\({\varvec{Q}}\) 的现有探索性方法必须预先指定属性的数量K。我们提出了一个贝叶斯框架来共同推断属性的数量K和\({\varvec{Q}}\)的元素。我们提出了压接采样算法来在K 的不同维度之间进行转换，并在强制执行模型可识别性约束的同时估计潜在的\({\varvec{Q}}\)和模型参数。我们还采用印度自助餐过程和可逆跳跃马尔可夫链蒙特卡罗方法来估计\({\varvec{Q}}\)。我们报告了压接采样器在三种方法中表现最好的证据。我们将开发的方法应用于两个数据集，并讨论这些发现对未来研究的影响。