A Parameteric, Hierarchical Statistical Framework for Inference with Skewed Distributions

该项目旨在开发一类统计模型，用于分析具有倾斜分布的数据，特别是来自分层或多级设置的数据。歪斜分布在社会科学中无处不在。通常，分布的高阶特征，如规模（可变性）和形状，可以提供对实质性问题的重要见解，并提供重要的理论发展。除了存在倾斜之外，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聚类，完成时间数据可以按参与者聚类。这些情况下的数据通常使用线性模型（如回归或方差分析）进行分析。尽管这些方法可以解释数据的层次性质，并且通常非常适合分析平均值的差异，但很难（如果不是不可能的话）对高阶特征进行推理。研究小组将开发一种贝叶斯方法来分析一类广泛的模型，其中关于位置、规模和形状的统计推断是可能的和实用的。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了解，即“先验分布”。在某些情况下，贝叶斯分析对这个先验相对不敏感；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。由于这些原因，研究团队将开发适当的“非信息性先验”。该项目将产生软件工具，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，研究人员有一套完善的统计工具来分析操纵对结果的总体影响。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绩效的可变性或绩效模式的偏差（如果在许多试验中表现良好而在少数试验中表现不佳，则会出现偏差）。该项目的目标是开发统计工具，以评估结果测量的变异性和偏差差异以及由于操纵造成的总体影响。研究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，预测实践影响表现可变性的学习理论可以经过严格的测试。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、教育学、经济学和其他社会科学。

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.