Multidimensional Latent Variable Models for Large and Complex Event History Data

该项目由两部分组成，这两部分由教育评估和健康科学推动并适用于这两部分。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与计算机互动的虚拟环境中解决问题的综合技能。现有的评估方法只着眼于最终答案，忽略了在互动过程中收集的大量行为数据。研究的第一部分探索了个体解决问题的整个互动过程，以便更有效和更准确地评估综合问题解决技能。开发的新工具将对国家和国际大规模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)和国际学生评估方案(PISA)，这两项评估计划是关于中小学教育的两个最重要的评估计划。第二部分开发了分析大规模卫生系统数据的新的统计方法。这些新的发展可以用来确定疗效和监测目前用于医疗保健管理计划的药物的副作用。它们还可能带来新的统计工具，用于分析行为数据，这在社会科学研究中很常见。该项目为研究生提供了研究培训机会。研究开发了中高维统计过程数据的潜变量模型和协变量和事件都稀疏时统计过程数据的动态回归模型。对于潜在变量/因子模型，本研究通过寻找合适的约束条件来解决可辨识性的基本和挑战性问题，这也导致了更简明和可解释的模型。在适当的正则性条件下，通过建立关键的渐近结果，发展了有效的推理方法。为了有效地进行参数估计，构造了基于随机梯度的算法。对于具有脆弱和动态协变量的多维计数过程模型，本研究从事件和协变量两个方面解决了稀疏性的挑战性问题。通过探索这些数据所固有的某些特殊结构，本研究为参数估计建立了适当的归一化渐近理论，以便进行有效的推理。协变量的稀疏性和相关的脆弱性使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，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.