Restricted latent class models (RLCMs) provide an important framework for diagnosing and classifying respondents on a collection of multivariate binary responses. Recent research made significant advances in theory for establishing identifiability conditions for RLCMs with binary and polytomous response data. Multiclass data, which are unordered nominal response data, are also widely collected in the social sciences and psychometrics via forced-choice inventories and multiple choice tests. We establish new identifiability conditions for parameters of RLCMs for multiclass data and discuss the implications for substantive applications. The new identifiability conditions are applicable to a wealth of RLCMs for polytomous and nominal response data. We propose a Bayesian framework for inferring model parameters, assess parameter recovery in a Monte Carlo simulation study, and present an application of the model to a real dataset.

受限潜在类别模型 (RLCM) 提供了一个重要的框架，用于根据多元二元响应集合对受访者进行诊断和分类。最近的研究在利用二元和多级响应数据建立 RLCM 的可识别性条件方面取得了重大理论进展。多类数据是无序的名义反应数据，在社会科学和心理测量学中也通过强制选择清单和多项选择测试广泛收集。我们为多类数据的 RLCM 参数建立了新的可识别性条件，并讨论了其对实质性应用的影响。新的可识别性条件适用于大量 RLCM 的多部分和名义响应数据。我们提出了一个用于推断模型参数的贝叶斯框架，评估蒙特卡罗模拟研究中的参数恢复，并提出该模型在真实数据集上的应用。