一种适用于多级反应、多级属性及协变量的受限潜在类别隐马尔可夫模型：可识别性及应用 (A Restricted Latent Class Hidden Markov Model for Polytomous Responses, Polytomous Attributes, and Covariates: Identifiability and Application)

from arxiv, 60 pages, 3 figures, 35 tables; added information on software and run times, expanded discussion section, cleaned up table headers and typos

We introduce a restricted latent class exploratory model for longitudinal data with ordinal attributes and respondent-specific covariates. Responses follow a time inhomogeneous hidden Markov model where the probability of a particular latent state at a time point is conditional on values at the previous time point of the respondent's covariates and latent state. We prove that the model is identifiable, state a Bayesian formulation, and demonstrate its efficacy in a variety of scenarios through two simulation studies. We apply the model to response data from a mathematics examination, comparing the results to a previously published confirmatory analysis, and also apply it to emotional state response data which was measured over a several-day period.

翻译：本文提出一种针对具有序数属性及受访者特定协变量的纵向数据的受限潜在类别探索性模型。反应遵循时间非齐次隐马尔可夫模型，其中特定时间点的潜在状态概率取决于受访者协变量与潜在状态在前一时间点的取值。我们证明了该模型的可识别性，阐述了其贝叶斯形式，并通过两项模拟研究展示了其在多种场景下的有效性。我们将该模型应用于数学考试的反应数据，将结果与先前发表的验证性分析进行对比，同时将其应用于持续数日测量的情绪状态反应数据。