Department of Mathematics and Statistics, University of Nevada, Reno, 1664 N. Virginia Street, Reno, NV, 89557, USA.
Department of Statistics, University of Illinois at Urbana-Champaign, 725 South Wright Street, Champaign, IL , 61820, USA.
Psychometrika. 2021 Mar;86(1):30-64. doi: 10.1007/s11336-021-09750-9. Epub 2021 Mar 22.
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.
诊断分类模型（DCM）广泛用于对多维离散属性集合进行细粒度分类。DCM 的应用需要在所谓的 [公式：见文本] 矩阵中指定潜在结构。专家指定的 [公式：见文本] 矩阵可能存在偏差，并导致不正确的诊断分类，因此一个关键问题是开发估计 [公式：见文本] 的方法，以便推断潜在属性和项目之间的关系。现有的用于估计 [公式：见文本] 的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，以联合推断属性的数量 K 和 [公式：见文本] 的元素。我们提出了卷曲抽样算法，以在不同的 K 维度之间进行转换，并在强制模型可识别性约束的同时估计潜在的 [公式：见文本] 和模型参数。我们还采用了印度自助餐过程和可逆跳转马尔可夫链蒙特卡罗方法来估计 [公式：见文本]。我们报告的证据表明，卷曲抽样器在这三种方法中表现最好。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意义。
