Bayesian Estimation of Restricted Latent Class Models for Ordinal and Nominal Response Data

该研究项目将推进统计模型和机器学习算法，用于描述人类反应数据的结构。工业界和学术界的决策者和研究人员收集并使用大规模数据集来了解人类行为。当前的方法提取潜在结构已知的响应数据的基本配置文件。然而，潜在的结构是很少知道的，所以现有的方法是适当的，只有在少数狭义的情况下。该项目将制定探索性方法，在潜在结构未知的情况下确定共同模式和概况。该研究将对健康人群和临床人群产生广泛影响，特别是为决策者提供精细信息，以加速人类发展和提高生活质量。将要开发的方法将应用于涉及认知表现的个体差异，影响大学生学术行为的心理因素和患者健康结果的数据。研究生将参与研究的进行。该研究项目将开发和应用统计模型，以便对人类反应数据中的系统模式进行精确、强大的建模和假设检验。将针对广泛的人类反应数据（包括顺序评级、排名和名义选择）研究限制性潜在类别模型（RLCM）。将开发用于估计一般RLCM的有序和名义响应数据的潜在结构的方法。贝叶斯方法将用于通过提供一个灵活的框架，探索潜在的结构，以改善现有的模型。项目创新将包括建立新的可识别性理论和研究潜在结构中的有序规范。从这项研究中获得的见解可能会导致潜在结构模型估计的基础统计理论的重大发展。这一理论的进步将对教育和心理学之外的广泛应用产生影响，包括其他社会科学学科和机器学习应用，这些应用根据底层特征对多变量名义数据进行聚类。研究人员将被提供工具，将潜在的结构与其他标准，如学术成功，有效的决策，和健康成果。这个奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

This research project will advance statistical models and machine learning algorithms used to describe the structure underlying human response data. Decision makers and researchers in industry and academia collect and use large-scale datasets to understand human behavior. Current methods extract profiles underlying response data where the latent structure is known. However, the latent structure is rarely known, so existing methods are appropriate in only a few narrowly defined cases. The project will develop exploratory methods for identifying common patterns and profiles when the latent structure is unknown. The research will have broad implications in healthy populations and in clinical populations, particularly in providing decision makers with fine-grained information to accelerate human development and improve quality of life. The methods to be developed will be applied to data involving individual differences in cognitive performance, psychological factors that influence college student academic behavior, and patient health outcomes. Graduate students will be involved in the conduct of the research. Publicly available software will be developed to provide researchers and decision makers with cutting-edge tools.This research project will develop and apply statistical models that will enable precise, powerful modeling and testing of hypotheses about systematic patterns in human response data. Restricted latent class models (RLCMs) will be investigated for a broad range of human response data, including ordinal ratings, rankings, and nominal choices. Methods for estimating the latent structure for general RLCMs for ordinal and nominal response data will be developed. Bayesian methods will be used to improve upon existing models by offering a flexible framework that explores the underlying structure. Project innovations will include establishing new identifiability theory and investigating ordinal specifications in the latent structure. Insights gained from this research could lead to significant developments in the underlying statistical theory for estimation of latent structure models. Advances in this theory will have implications for a broad spectrum of applications beyond education and psychology, including other social science disciplines and machine learning applications that cluster multivariate nominal data according to underlying features. Researchers will be provided with tools to relate the latent structure to other criteria, such as academic success, effective decision-making, and health outcomes.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.