Collaborative Research: Modeling Unobserved Heterogeneity in Network Formation

网络的统计分析在社会和行为科学中变得越来越重要，近年来已被应用于各种问题。事实上，国家科学基金会的社会科学议程设置声明“重建马赛克”将网络科学视为四个关键研究前沿之一。然而，虽然网络的统计分析继续吸引学者和广大公众的大量关注，网络的定量研究仍处于发展的早期阶段。直到最近，统计理论和计算技术才得以发展，以严格分析各种类型的网络。该项目的中心目标是开发一个新的模型，用于识别网络形成的统计影响，明确说明未观察到的变化。技术摘要PI开发了一种估计器，可以准确捕获网络模型中连接形成中未观察到的异质性。他们通过扩展广泛应用的指数随机图模型（ERGM）来实现这一点，以包括一个脆弱项，该脆弱项解释了未测量、未观察或无法想象的异质性。未考虑的异质性是社会过程研究中的一个重要问题;因此，无法有效地建模是一个重要的差距，限制了ERGMs在许多潜在领域的适用性。事实上，ERGM的两个主要假设之一是模型被正确地指定，并且系数偏差或模型退化可能由违反此假设而导致。PI建议通过引入脆弱项来扩展ERGM以解决这个问题，从而创建脆弱指数随机图模型（FERGM）。除了定义FERGM和提供蒙特卡洛模拟来证明模型属性和方法的比较优势外，PI还将FERGM应用于社会和健康科学的实质性主题，并为其他人提供相关的统计软件。网络建模的进步将在科学学科中发挥作用，包括社会学，经济学，统计学，计算机科学和行为健康。对社会科学应用的关注将有助于公共政策的实践者，使他们能够更准确地评估政策对经济和社会成果的重要性。最后，该项目直接促进教学、培训和学习，并扩大代表性不足的群体对学术活动的参与。

General SummaryThe statistical analysis of networks has become increasingly important in the social and behavioral sciences and has been applied to a diverse range of problems in recent years. Indeed, the National Science Foundation's agenda setting statement for the social sciences, "Rebuilding the Mosaic," recognizes Network Science as one of four critical research frontiers. Yet, while the statistical analysis of networks continues to attract a great deal of attention from scholars and the broader public, the quantitative study of networks remains in the early stages of development. Only recently have the statistical theory and computational techniques been developed to rigorously analyze various types of networks. The central aim of the project is to develop a new model for identifying statistical effects on network formation that explicitly accounts for unobserved variation. Technical SummaryThe PIs develop an estimator that accurately captures unobserved heterogeneity in tie formation in network models. They do so by extending the widely applied Exponential Random Graph Model (ERGM) to include a frailty term that accounts for unmeasured, unobserved, or unimagined heterogeneity. Unaccounted heterogeneity is a significant issue in the study of social processes; thus, the inability to effectively model it is an important gap that limits the applicability of ERGMs in many areas of potential interest. In fact, one of the two major assumptions of the ERGM is that the model is correctly specified, and coefficient bias or model degeneracy may result from violations of this assumption. The PIs propose to extend the ERGM to account for this problem through the introduction of a frailty term, thereby creating a Frailty Exponential Random Graph Model (FERGM). In addition to defining the FERGM and providing Monte Carlo simulations to demonstrate the model properties and comparative benefits of the approach, the PIs apply the FERGM to substantive topics in the social and health sciences and provide related statistical software for others to do so as well. Advances in network modeling will be useful across scientific disciplines, including sociology, economics, statistics, computer science and behavioral health. The focus on social science applications will aid practitioners in public policy by allowing them to more accurately evaluate the importance of policy on economic and social outcomes. Finally, the project directly promotes teaching, training, and learning and broadens participation of underrepresented groups in scholarly activity.