Nonparametric Models and Methods for Social Sciences Data

社会科学家经常收集和分析纵向的数据。一些纵向研究的持续时间较长，这导致每个受试者都有大量的观察，并产生了所谓的功能数据。除了缺乏独立性外，这种数据的分析往往很复杂，原因有两个。首先，对于许多类型的社会科学数据，有一些关于函数形式的薄弱理论来解释因素的影响，以及产生顺序或仅略强(但通常不是区间)的弱测量程序(例如，态度)的影响。因此，需要对非正态且通常是异方差的数据进行灵活的建模和检验程序。其次，当受试者被跟踪很长一段时间时，遗漏观察是很常见的。通常，“缺失”不是完全随机的，这会导致参数类型的补救措施。在这个项目中，研究人员提出了一种完全非参数的方法来解决关于这些数据的一些推断问题。他们将考虑a)当某些(或全部)因素具有多个水平但每个细胞的重复数很少时的方差设计的多向异方差分析的推断程序，b)因协变量的存在而调整的因素的影响，c)协变量效应及其与分类因素的相互作用，以及d)缺失数据的设计。还将针对上述问题开发使用(中等)等级加权平均数并已知对各种数据类型保持较高效率的程序。该项目的各个方面与缺乏适合性测试的经典问题密切相关，将开发的一些方法也将与这一领域相关。这项研究建立在研究人员先前的研究成果的基础上，其中许多是通过先前的授权获得的。非参数方法提供的灵活的建模，以及(中级)检验统计量提供的有效的检验程序，是本项目的关键推动力。为了确定几个分类因素和连续协变量对感兴趣反应的影响，研究人员通常使用参数或半参数事件历史模型，包括线性模型、广义线性模型、脆弱性模型、边际比例风险模型和随机系数模型。这些模型所依赖的假设对于任何给定的应用程序都可能满足，也可能不满足。正如几个案例研究所记录的那样，这可能会产生令人不快的实际后果。此外，缺失的观测值需要用参数假设进行推算。事实上，人们普遍认为，当数据随机丢失(而不是完全随机丢失)时，不能使用非参数程序。将制定实施非参数程序的方案，并将其应用于一些社会科学研究，包括a)关于日常活动和越轨行为的问题，b)检查各种生活环境对刑事犯罪的影响，以及c)检查最近从惩教机构释放的被监禁男孩。该奖项由数学科学司和社会、行为和经济科学局共同支持，作为数学科学优先领域的一部分。

Social scientists often collect and analyze data that are longitudinal. Some longitudinal studies have long durations, which result in large number of observations per subject and give rise to what is called functional data. The analysis of such data often is complicated for two reasons in addition to the lack of independence. First, for many kinds of social science data, there are weak theories about functional forms explaining the effects of factors and weak measurement procedures (e.g., with attitudes) that produce ordinal or only somewhat stronger (but typically not interval) scales. Thus, there is need for flexible modeling and test procedures for non-normal and often heteroscedastic data. Second, missing observations are common whenever subjects are followed for long periods. Typically, "missingness" is not completely at random, causing parametric-type remedies. In this project, the investigators propose a fully nonparametric approach to some inference questions regarding such data. They will consider inference procedures for a) multi-way heteroscedastic analysis of variance designs when some (or all) of the factors have many levels but small number of replications per cell, b) the effects of factors which adjust for the presence of covariates, c) the covariate effect and its interaction with categorical factors, and d) designs with missing data. Procedures that use weighted averages of (mid-) ranks and that are known to maintain a high level of efficiency for a wide variety of data types will also be developed for the above problems. Facets of the project are closely connected to the classical problem of lack-of-fit testing and some methods that will be developed also will be relevant in this area. This research builds upon prior results by the investigators, many of which were obtained using previous grants.The flexible modeling provided by the nonparametric approach, coupled with the efficient test procedures afforded by (mid-) rank test statistics, are the key thrusts of this project. To ascertain the effect of several categorical factors and continuous covariates on a response of interest, researchers typically use parametric or semiparametric event history modeling, including linear models, generalized linear models, frailty models, marginal proportional hazards models, and random coefficient models. These models depend on assumptions that may or may not be satisfied for any given application. This can have unpleasant practical consequences as documented in several case studies. Moreover, missing observations require imputations that are done with parametric assumptions. In fact, it is widely believed that nonparametric procedures cannot be used when data are missing at random (as opposed to missing completely at random). Programs for implementing the nonparametric procedures will be developed and applied to a number of social sciences studies including a) questions regarding routine activities and deviant behavior, b) examination of the effects of various life circumstances on criminal offending, and c) examination of incarcerated boys recently released from correctional institutions. This award is jointly supported by the Division of Mathematical Sciences and the Directorate for Social, Behavioral, and Economic Sciences as part of the Mathematical Sciences Priority Area.