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往往具有多层次或嵌套结构的特点，在这种结构中，较低级别的单位属于且只有一个较高级别单位；例如，学生就读于一所且仅一所学校，患者由且仅由一家卫生保健提供者治疗。嵌套数据的传统多水平建模目前已被人们所熟知，并被频繁地应用于不同的研究领域。然而，许多数据结构是多层次的，但不符合嵌套的条件：学生可能会上不止一所学校，病人可能会由不止一个医疗保健提供者治疗。交叉分类，多成员(CCMM)建模是由Browne，Goldstein和Rasbash(2001)提出的用于多水平非嵌套数据建模的通用统计框架。它在许多研究领域具有广泛的潜在应用，包括教育、卫生研究和流行病学、社会学和人类遗传学。虽然CCMM建模的应用已经开始在文献中出现，但CCMM建模的统计方面还没有得到广泛的研究，建模的实际经验仍然非常有限。本文的研究将评估CCMM模型的估计性能，并使用实际数据分析和蒙特卡罗模拟来研究忽略多层非嵌套数据结构的后果。CCMM模型将应用于幼儿纵向学习幼儿园队列(ECLS-K)数据，以模拟在纳入学生流动性后从幼儿园到五年级的阅读和数学成长。在真实数据分析的指导下，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数据结构的操纵数据条件下忽略CCMM数据结构的后果。将编写用户友好的计算机程序代码和分步教程，以促进CCMM建模在应用研究中的使用。这项研究不仅包括对复杂数据结构的高级统计建模及其应用的最新回顾，而且还首次系统地研究了基于贝叶斯估计的多水平非嵌套数据的CCMM建模的统计性能。它将展示CCMM建模在分析多级别非嵌套数据方面的灵活性，并导致在实际研究环境中对复杂数据进行适当建模的科学知识的进步。使用ECLS-K进行的实际数据分析将展示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。蒙特卡洛模拟研究将为研究界提供关于CCMM模型的统计性能的证据和关于CCMM模型建立的方法学指导，这最终将有助于将创新的量化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，独立的研究事业。

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.