A Parameteric, Hierarchical Statistical Framework for Inference with Skewed Distributions

用于倾斜分布推理的参数化分层统计框架

• 批准号: 0095919
• 负责人: Jeffrey Rouder
• 金额: $ 30万
• 依托单位: University of Missouri-Columbia
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-03-15 至 2005-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0095919&HistoricalAwards=false
• 关键词: Parameteric; Hierarchical; Statistical; Framework; Inference

This project seeks to develop a class of statistical models for the analysis of data having skewed distributions, especially data arising from hierarchical or multi-level settings. Skewed distributions are ubiquitous in the social sciences. Often, the higher-order characteristics of the distribution, such as the scale (variability) and shape, can provide important insight into substantive issues and provide for significant theoretical development. In addition to having skew, these distributions typically have variability at several levels. For example, businesses may be clustered by economic sectors and completion time data may be clustered by participant. Data in these contexts often are analyzed with linear models such as regression or ANOVA. Although these methods can account for the hierarchical nature of the data and often are well-suited to analyzing differences in means, it is difficult, if not impossible, to perform inference on higher order characteristics. The researcher team will develop a Bayesian approach to analyzing a broad class of models in which statistical inference about location, scale, and shape is both possible and practical. Bayesian statistics is adopted because it is ideally suited to hierarchical models. Bayesian analysis depends on the researcher's informed knowledge of experimental conditions -- the "prior distribution." In some cases, Bayesian analysis is relatively insensitive to this prior; however, in other cases subtle errors in prior specification can lead to erroneous inference. For these reasons, the research team will develop appropriate "noninformative priors." The project will produce software tools so that other researchers can perform Bayesian analysis on these hierarchical models.In the social sciences, researchers have a well-developed set of statistical tools for analyzing the overall effects of manipulations on outcomes. For example, experimental psychologists study how practice (a manipulation) improves performance (an outcome). Current statistical tools are well-suited for assessing the overall (e.g., average) improvement with practice but are ill-suited for assessing whether practice affects the variability of performance or the skew in the pattern of performance (skew would occur if performance is good on many trials and poor on a few). The goal of the project is the development of statistical tools for assessing differences in variability and skew of outcome measures as well as overall effects due to manipulations. The results will lead not only to better understanding of the data but, more importantly, to better theoretical development. For example, learning theories which predict that practice affects the variability of performance can be rigorously tested. The developed statistical tools would be broad and applicable to many social science fields such as psychology, education, economics, and other social sciences.

该项目旨在开发一类统计模型，用于分析具有偏斜分布的数据，特别是来自分层或多级设置的数据。 偏态分布在社会科学中无处不在。 通常情况下，分布的高阶特征，如规模（可变性）和形状，可以提供重要的洞察实质性问题，并提供重要的理论发展。 除了具有偏斜之外，这些分布通常在几个水平上具有可变性。 例如，企业可以按经济部门聚类，完成时间数据可以按参与者聚类。 在这些背景下的数据通常使用线性模型进行分析，例如回归或ANOVA。 虽然这些方法可以解释数据的分层性质，并且通常非常适合于分析平均值的差异，但很难（如果不是不可能的话）对高阶特征进行推断。 研究小组将开发一种贝叶斯方法来分析广泛的一类模型，其中关于位置，规模和形状的统计推断既可能又实用。 采用贝叶斯统计是因为它非常适合分层模型。 贝叶斯分析依赖于研究人员对实验条件的知情知识--“先验分布”。在某些情况下，贝叶斯分析对这种先验相对不敏感;然而，在其他情况下，先验规范中的细微错误可能导致错误的推断。 由于这些原因，研究小组将开发适当的“非信息先验”。他说：“这项计划将制作软件工具，让其他研究人员可以对这些分层模型进行贝叶斯分析。在社会科学方面，研究人员有一套完善的统计工具，可以分析操纵对结果的整体影响。 例如，实验心理学家研究练习（操纵）如何提高表现（结果）。 目前的统计工具非常适合于评估整体（例如，平均值）的改进，但不适合评估实践是否影响性能的可变性或性能模式中的偏斜（如果性能在许多试验中良好而在少数试验中较差，则会发生偏斜）。 该项目的目标是开发统计工具，用于评估结果测量的变异性和偏斜的差异以及由于操纵而产生的总体影响。 这些结果不仅有助于更好地理解数据，更重要的是，有助于更好地发展理论。 例如，预测实践会影响表现可变性的学习理论可以得到严格的检验。 开发的统计工具将广泛适用于许多社会科学领域，如心理学，教育，经济学和其他社会科学。