A Parameteric, Hierarchical Statistical Framework for Inference with Skewed Distributions

该项目旨在开发一类统计模型，用于分析具有偏态分布的数据，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普遍存在。通常，分布的高阶特征，如规模(变异性)和形状，可以提供对实质性问题的重要洞察，并为重大理论发展提供依据。除了具有不对称性之外，这些分布通常在几个级别上具有可变性。例如，企业可以按经济部门分类，完成时间数据可以按参与者分类。这些情况下的数据通常使用回归或方差分析等线性模型进行分析。虽然这些方法可以解释数据的层次性，并且往往非常适合于分析手段上的差异，但对高阶特征进行推断即使不是不可能，也是困难的。研究小组将开发一种贝叶斯方法来分析一大类模型，在这些模型中，关于位置、规模和形状的统计推断既可能又实用。贝叶斯统计之所以被采用，是因为它非常适合于分层模型。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，贝叶斯分析对这一先验相对不敏感；然而，在其他情况下，先前规范中的细微错误可能导致错误的推断。出于这些原因，研究团队将开发适当的“非信息性前科”。该项目将生产软件工具，以便其他研究人员可以对这些分层模型进行贝叶斯分析。在社会科学领域，研究人员拥有一套完善的统计工具，用于分析操纵对结果的整体影响。例如，实验心理学家研究练习(一种操作)如何提高表现(一种结果)。目前的统计工具非常适合于评估实践的总体(例如，平均)改进，但不适合评估实践是否影响业绩的可变性或业绩模式的偏差(如果多次试验的业绩好，少数试验的业绩差，就会出现偏差)。该项目的目标是开发统计工具，用于评估结果衡量的可变性和偏斜性的差异以及因操纵而产生的总体影响。研究结果不仅将有助于更好地理解数据，更重要的是，将有助于更好的理论发展。例如，预测实践会影响表现变异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心理学、教育学、经济学和其他社会科学等许多社会科学领域。

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.