Multidimensional Latent Variable Models for Large and Complex Event History Data

该项目由两部分组成，这两部分的动机和适用于教育评估和健康科学。现代计算机和信息技术的进步使教育评估能够衡量考生在虚拟环境中与计算机交互体验的综合解决问题的能力。现有的评估方法只看最终的答案，忽略了在交互过程中收集的大量行为数据。研究的第一部分探讨了个体的整个互动问题解决过程，以便更有效和更准确地评估综合问题解决技能。所开发的新工具将对大规模国家和国际教育评估的设计和分析产生直接影响，如国家教育进展评估（NAEP）和国际学生评估计划（比萨），这是两个最重要的中小学教育评估计划。第二部分开发了新的统计方法来分析大规模卫生系统数据。新的发展可用于确定疗效和监测目前在医疗保健管理计划中使用的药物的副作用。它们还可能导致用于分析行为数据的新统计工具，这在社会科学研究中很常见。本研究为研究生提供研究训练的机会，针对中高维计数过程数据建立潜变量模型，并针对协变量和事件均为稀疏时的计数过程数据建立动态回归模型。对于潜变量/因子模型，该研究通过找到合适的约束来解决可识别性的基本和具有挑战性的问题，这也导致了更简约和可解释的模型。通过在适当的正则性条件下建立关键的渐近结果，得到了有效的推论方法。随机梯度为基础的算法构造有效地进行参数估计。对于具有脆弱性和动态协变量的多维计数过程模型，研究解决了具有挑战性的稀疏性问题，在事件和协变量方面。通过探索这些数据中固有的某些特殊结构，研究建立了适当的归一化渐近理论的参数估计，以便进行有效的推断。协变量的稀疏性和相关的脆弱性使得渐近理论具有挑战性，因为用于计算过程模型的标准技术不再适用。该奖项反映了NSF的法定使命，并被认为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来支持。

The project consists of two parts which are motivated by and applicable to educational assessment and health sciences. Advances in modern computer and information technology enable educational assessments to measure comprehensive problem-solving skills in virtual environments in which examinees experience interactively with computers. The existing evaluation methods only look at the final answers, ignoring vast behavioral data collected over the course of interaction. The first part of the research explores the entire interactive problem-solving processes by individuals so that comprehensive problem-solving skills can be assessed efficiently and more accurately. The developed new tools will have direct impacts on the design and analysis of large scale national and international educational assessments such as the National Assessment of Educational Progress (NAEP) and the Programme for International Student Assessment (PISA), which are the two most important assessment schemes on the primary and secondary education. The second part develops novel statistical approaches to analyzing large scale health system data. The new developments could be used to ascertain efficacy and monitor side effects for drugs currently used in healthcare management programs. They could also lead to new statistical tools for analyzing behavioral data, which are common in social science studies. The project provides research training opportunities for graduate students.The research develops latent variable models for moderately high dimensional counting process data and dynamic regression models for counting process data when both covariates and events are sparse. For latent variable/factor models, the research addresses the fundamental and challenging issue of identifiability by finding suitable constraints, which also lead to more parsimonious and interpretable models. Valid inferential methods are developed by establishing crucial asymptotic results under appropriate regularity conditions. Stochastic gradient-based algorithms are constructed for efficiently carrying out parameter estimation. For the multidimensional counting process models with frailty and dynamic covariates, the research addresses the challenging issue of sparsity, in terms of both events and covariates. By exploring certain special structures inherent in such data, the research establishes suitably normalized asymptotic theories for parameter estimation so that valid inference can be conducted. The covariate sparsity and correlated frailty make the asymptotic theory challenging as standard techniques used for counting process models are no longer appropriate.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.