Nonparametric Models and Methods for Social Sciences Data

社会科学数据的非参数模型和方法

• 批准号: 0318200
• 负责人: Michael Akritas
• 金额: $ 23.42万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-09-01 至 2007-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0318200&HistoricalAwards=false
• 关键词: Nonparametric; Models; Methods; Social; Sciences

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.

社会科学家经常收集和分析纵向数据。 一些纵向研究持续时间较长，这导致每个受试者的大量观察结果，并产生所谓的功能数据。 除了缺乏独立性之外，由于两个原因，对这类数据的分析往往很复杂。 首先，对于许多类型的社会科学数据，关于解释因素影响的函数形式和薄弱的测量程序（例如，与态度），产生顺序或只是稍微强（但通常不是间隔）规模。 因此，需要灵活的建模和测试程序的非正常的，往往异方差数据。 第二，观察结果缺失是常见的，只要受试者被跟踪很长一段时间。 通常，“缺失”并不是完全随机的，导致参数型补救措施。 在这个项目中，研究人员提出了一个完全非参数的方法来推断有关这些数据的一些问题。 他们将考虑a）当某些（或所有）因子具有多个水平但每个单元格的重复次数较少时的多因素异方差分析设计的推理程序，B）针对协变量存在进行调整的因子的效应，c）协变量效应及其与分类因子的相互作用，以及d）缺失数据的设计。 还将为上述问题开发使用（中间）等级加权平均值的程序，这些程序已知可对各种数据类型保持高水平的效率。 该项目的各个方面与经典的失拟检验问题密切相关，将开发的一些方法也将与该领域相关。 这项研究建立在以前的研究结果，其中许多是使用以前的赠款灵活的建模提供的非参数方法，再加上有效的检验程序提供的（中）秩检验统计，是这个项目的关键推力。 为了确定几个分类因子和连续协变量对感兴趣的响应的影响，研究人员通常使用参数或半参数事件历史建模，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。 这些模型依赖于可能满足或可能不满足任何给定应用的假设。 正如若干案例研究所述，这可能产生令人不快的实际后果。 此外，缺失观察值需要使用参数假设进行插补。 事实上，人们普遍认为，当数据随机缺失时（与完全随机缺失相反），不能使用非参数程序。 实施非参数程序的程序将被开发并应用于一些社会科学研究，包括a）关于日常活动和异常行为的问题，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。 该奖项由数学科学部和社会，行为和经济科学理事会共同支持，作为数学科学优先领域的一部分。