Bayes Factor Methods for Model Comparison in the Social Sciences

该项目将为常见的研究设计开发贝叶斯因子。贝叶斯因子提供了一个有吸引力的替代传统显著性检验，特别是线性模型的f检验。然而，由于至少两个原因，它们未能获得广泛的接受：它们被认为对所选择的先验分布有不良的依赖，并且它们被认为难以计算。为了解决第一个问题，将开发一类“默认”先验的贝叶斯因子；也就是说，在先验条件下，贝叶斯因子具有理想的理论性质，传递最小程度的信息，并且广泛适用于广泛的常见设计。理想先验的一个自然属性是“一致性”，即在大样本限制下支持正确模型的能力。当模型维度与样本量相比相对较大时，重点是一致性，这在许多ANOVA设计中很常见。一致性将在常见的单向和双向以及可能的高阶设计中得到证明。关于第二个问题，计算可能需要跨多个维度进行集成。有几种选择（包括正交、蒙特卡罗采样、桥式采样、拉普拉斯近似或Savage-Dickey密度比估计），哪种选择效果最好取决于样本量和设计。将开发用于选择快速有效的计算方法的启发式方法。最终的结果将是开发出易于计算且性能优异的贝叶斯因子。物理科学通过识别不变性——即当其他元素发生变化时保持不变的元素——而取得了进展。相反，社会科学强调的是对效果的论证，而不是对不变性的论证。在嘈杂环境中证明不变性的一个困难是方法上的——传统的假设检验允许研究人员收集反对零的证据，但从来没有收集过支持零的证据。贝叶斯因子提供了一个理想的解决方案，因为它们可以用来评估零值或替代值的证据，解释起来很简单，并且为模型复杂性提供了自然的惩罚。该项目的最终目标是使贝叶斯因子成为实质性研究人员方法论工具包中广泛采用的日常方法。为此，该项目将开发一系列软件应用程序。其中一些将是面向方法学家的R包。其他将是面向没有统计专业知识的实质性研究人员的web小程序和GUI软件。后一种产品将非常容易使用，这种易用性应该会鼓励快速采用。此外，还计划在调查人员各自的学科中举办会议讲习班和辅导课，包括短期课程。

The project will develop Bayes factors for common research designs. Bayes factors provide an attractive alternative to conventional significance tests, in particular to F-tests for linear models. They have failed, however, to achieve broad acceptance for at least two reasons: They are perceived as having an undesirable dependence on the chosen prior distribution, and they are viewed as being difficult to compute. To address the first concern, Bayes factors for a class of "default" priors will be developed; this is, with priors that result in Bayes factors with desirable theoretical properties, impart a minimal degree of information, and are broadly applicable in a wide range of common designs. One natural property of a desirable prior is "consistency," the ability to support the correct model in the large sample limit. The focus is on consistency when the model dimension is relatively large compared to the sample size, as is common in many ANOVA designs. Consistency will be proved for common one-way and two-way and possibly higher order designs. With respect to the second concern, computation entails integration across perhaps many dimensions. There are several choices (including quadrature, Monte Carlo sampling, bridge sampling, Laplace approximation, or Savage-Dickey density ratio estimation), and which choice works best will vary depending on the sample size and design. Heuristics for picking a method of computation that is quick and efficient will be developed. The end result will be the development of easy-to-compute Bayes factors with excellent properties.The physical sciences have made gains by identifying invariances -- those elements that stay constant when others change. In contrast, the social sciences have emphasized demonstrations of effects rather than of invariances. One difficulty in demonstrating invariances in noisy environments is methodological -- conventional hypothesis testing allows researchers to amass evidence against the null but never for it. Bayes factors provide an ideal solution because they can be used to assess evidence for the null or alternative, are straightforward to interpret, and provide a natural penalty for model complexity. The project's ultimate goal is that Bayes factors become a widely-adopted, everyday method in substantive researchers' methodological toolkit. To that end, the project will develop a series of software applications. Some of these will be R packages for methodologists. Others will be web applets and GUI software for substantive researchers without statistical expertise. These latter products will be very easy to use, and this ease should encourage rapid adoption. In addition, conference workshops and tutorials, including short courses, are planned in the investigators' respective disciplines.