Collaborative Research: Nonparametric Models for Incomplete Clustered Data with Applications to the Social Sciences

聚类数据在社会科学研究和其他领域非常常见。例如，在一项涉及在校儿童的研究中，学区形成集群，学校在每个集群中形成子集群。在这种情况下，研究人员希望根据某些分类变量（因素）来解释某个感兴趣的变量（反应变量），同时调整可能影响反应的其他附带变量（协变量）的存在。这个项目的目的是发展分析这些数据的统计方法。虽然经典的统计方法适应了群集抽样产生的数据固有的缺乏独立性，但它们往往不适合来自社会科学研究的数据。这是因为它们需要一组限制性假设（如残差的正态性和同质性、线性、尺度依赖性），这些假设在社会科学中很少得到满足。此外，社会科学研究中的数据往往是不完整的（删节或缺失），在这种情况下，基于经典统计模型的推理无法实现。为处理这些问题而开发的替代方法也依赖于假设，这些假设可能满足也可能不满足任何给定的应用程序。该项目的研究将集中于发展不受限制性假设限制的统计模型和方法。该项目的核心组成部分是将这些方法应用于有关日常活动和越轨行为的问题，以及使用国家纵向调查（NLS）的两个队列来解决过去三十年中年轻人中工作不稳定性是否长期上升的问题。正式的假设检验程序，效果的图形总结和探索性数据分析图，将在网上提供给社会科学界使用。正确的统计分析非常重要，因为它经常构成政策和其他决定的基础。本项目中的非参数公式特别适用于许多类型的社会科学数据，其中我们有关于功能形式的弱理论和弱测量程序（例如，与态度），这些测量程序产生有序或仅稍微强一些（但通常不是区间）尺度。违反统计方法的假设可能导致滥用稀缺的数据资源，并最终导致错误的政策决定。

Clustered data are very common in social sciences research and other fields. For example, in a study involving school children, school districts form clusters and schools form sub-clusters within each cluster. In this context, researchers want to explain a certain variable of interest (the response variable) in terms of certain categorical variables (factors) while adjusting for the presence of other incidental variables (covariates) which might influence the response. This project aims at developing statistical methods for analyzing such data. Though the classical statistical methods accommodate the lack of independence that is inherent to data arising from cluster sampling, they are very often unsuitable for data arising from social science research. This is because they require a set of restrictive assumptions (such as normality and homogeneity of the residuals, linearity, scale dependence) which are rarely satisfied in the social sciences. In addition, data in social sciences research are often incomplete (censored or missing) in which case inference based on the classical statistical models cannot be implemented. Alternative approaches developed to deal with these issues also rely on assumptions which may or may not be satisfied for any given application. The research for this project will focus on the development of statistical models and methods that are free of restrictive assumptions. Central components of the project is the application of these methods to questions regarding routine activities and deviant behavior, and to the question of whether there has been a secular rise in job instability among young adults over the past three decades using two cohorts from the National Longitudinal Survey (NLS). Programs for formal hypothesis testing, graphical summaries of effects and exploratory data analysis plots, will be made available on the web for use by the social sciences community.Correct statistical analysis is very important as it often forms the basis for policy and other decisions. The nonparametric formulation in this project is especially apt for many kinds of social science data where we have weak theories about functional forms and weak measurement procedures (e.g., with attitudes) that produce ordinal or only somewhat stronger (but typically not interval) scales. The violation of assumptions underlying a statistical approach can result in misuse of scarce data resources and ultimately misguided policy decisions.