Doctoral Dissertation Research: Cross-Classified, Multiple-Membership Modeling for Multilevel, Nonnested Data

在许多社会科学中收集的数据通常具有多层次或嵌套结构的特点，其中较低层次的单位属于一个且只有一个较高层次的单位;例如，学生参加一个且只有一个学校，患者由一个且只有一个医疗保健提供者治疗。 嵌套数据的传统多水平模型现在被很好地理解并经常应用于不同的研究领域。 然而，许多数据结构是多级的，但不符合嵌套的条件：学生可能参加一个以上的学校，病人可能由一个以上的医疗保健提供者治疗。 交叉分类、多重隶属（CCMM）建模是一种用于建模多层次、非嵌套数据的通用统计框架，由Browne、Goldstein和Rasbash（2001）提出。 它在许多研究领域有广泛的潜在应用，包括教育，健康研究和流行病学，社会学和人类遗传学。 虽然CCMM建模的应用已经开始出现在文献中，CCMM建模的统计方面还没有得到广泛的研究，模型构建的实践经验仍然非常有限。 本论文的研究将评估CCMM模型的估计性能，并研究忽略多级，非嵌套的数据结构，使用真实的数据分析和蒙特卡洛模拟的后果。 CCMM模型将应用于幼儿纵向研究幼儿园队列（ECLS-K）数据，以模拟从幼儿园到五年级的阅读和数学增长，并纳入学生的流动性。 在真实的数据分析的指导下，将进行全面的蒙特卡罗模拟，以评估CCMM建模的估计性能以及在模拟真实的数据结构的操纵数据条件下忽略CCMM数据结构的后果。 用户友好的计算机程序代码和一步一步的教程将被编写，以方便使用CCMM建模在应用research.This研究不仅包括先进的统计建模复杂的数据结构及其应用的最新审查，但也是第一个系统的调查CCMM建模的统计性能，多层非嵌套数据使用贝叶斯估计。 它将展示CCMM建模在分析多级非嵌套数据中的灵活性，并导致在真实的研究环境中对复杂数据进行适当建模的科学知识的进步。 ECLS-K的真实的数据分析将显示CCMM模型在应用研究中的适用性，并帮助教育工作者和研究人员更好地了解学生流动如何影响早期阅读和数学发展。 蒙特卡罗模拟研究将为研究界提供有关CCMM建模的统计性能和CCMM模型构建方法学指导的证据，最终将有助于将创新的定量研究方法转化为社会科学及其他领域的严格应用研究。 作为博士论文研究改进奖，提供支持，使有前途的学生建立一个强大的，独立的研究生涯。

Data collected in many social sciences often are characterized by multilevel or nested structures in which a lower-level unit belongs to one and only one higher-level unit; for instance, students attend one and only one school, and patients are treated by one and only one health care provider. Conventional multilevel modeling for nested data is now well understood and frequently applied in different research areas. However, many data structures are multilevel but do not qualify as nested: Students may attend more than one school, and patients may be treated by more than one health care provider. Cross-classified, multiple-membership (CCMM) modeling, a general statistical framework for modeling multilevel, nonnested data, was set forth by Browne, Goldstein, and Rasbash (2001). It has a wide range of potential applications in many research areas, including education, health research and epidemiology, sociology, and human genetics. Though applications of CCMM modeling have started to appear in the literature, the statistical aspects of CCMM modeling have not been investigated extensively, and the practical experiences of model building are still very limited. This dissertation research will evaluate the estimation performance of CCMM modeling and investigate the consequences of ignoring multilevel, nonnested data structures using both real data analyses and Monte Carlo simulation. CCMM modeling will be applied to the Early Childhood Longitudinal Study Kindergarten Cohort (ECLS-K) data to model reading and mathematics growth from kindergarten to fifth grade after incorporating student mobility. Guided by real data analyses, a comprehensive Monte Carlo simulation will be conducted to evaluate the estimation performance of CCMM modeling and consequences of ignoring CCMM data structures under manipulated data conditions that emulate real data structures. User-friendly computer program codes and step-by-step tutorials will be written to facilitate the use of CCMM modeling in applied research.This research includes not only a state-of-the-art review of advanced statistical modeling for complex data structures and their applications, but also the first systematic investigation of the statistical performance of CCMM modeling for multilevel nonnested data using Bayesian estimation. It will demonstrate the flexibility of CCMM modeling in analyzing multilevel nonnested data and lead to advancements of scientific knowledge regarding appropriate modeling of complex data in real research settings. The real data analyses with ECLS-K will show the applicability of CCMM modeling in applied research and help educators and researchers to better understand how student mobility affects early reading and mathematics development. The Monte Carlo simulation study will provide evidence regarding the statistical performance of CCMM modeling and methodological instructions on CCMM model building for the research community, which eventually will facilitate translating innovative quantitative research methods into rigorous applied research in the social sciences and beyond. As a Doctoral Dissertation Research Improvement award, support is provided to enable a promising student to establish a strong, independent research career.