Bayesian Models for Assessing Shape and Covariance in Behavioral Data

该项目将调查心理学研究中两个截然不同但相关的问题。第一个涉及响应时间(RT)，即完成实验任务所需的时间。反应时分布的形状是认知加工的关键标志。研究将开发统计方法来测试形状是不变的还是取决于协变量，如参与者的特征和实验操作。方法是从一大类三参数分布中选择合适的分布，这些分布来自Bar-Lev和Reiser引入的带有移位参数的两参数指数族。一种统一的方法将为这类非规则分布开发客观的贝叶斯方法。第二个关键的研究问题是关于人、物品和条件之间的潜在心理过程的关联。了解这些过程是如何相关的，将为理解认知提供洞察力。具体的问题是在分层设置中对两个或多个相关的双变量分布的协方差矩阵的关联进行建模。该项目将为这些协方差矩阵的贝叶斯分析开发客观先验，概括单变量信噪比先验的最新发展。该项目的两个阶段都涉及心理学认知研究中的基本和重要问题，以及对相关领域的潜在影响。对反应时间的研究也是发展心理学、社会心理学以及精神病理学研究的基础。关于这些领域的认知加工以及受试者的实验条件和特征是如何影响认知加工的，已经发展了许多理论。这些理论中的大多数预测了响应时间分布的形状变化。然而，这些分布的形状是否真的随着实验条件的响应而改变这一基本问题还没有被研究。了解响应时间分布形状是否以及如何变化将推动新的理论方向。此外，还将开发适用于心理学以外的有用的新统计方法。第二个问题是潜在变量协方差矩阵的估计，其动机是研究记忆任务中不同的回忆模式。给出要研究的单词列表并随后询问这些单词的参与者可能会因为可能基于先前的熟悉程度而做出“自动”响应，或者他们可能会基于实际的回忆而做出响应。这两个过程的评估是复杂的，因为一些单词可能同时更容易自动回忆或更容易记住；同样，人们可能会同时在自动反应或记忆方面表现得更好。对这些关系的评估是微妙和具有挑战性的。这项研究将对工作记忆和认知老化的心理学研究产生影响。此外，统计模型与流行病学、经济学和生态学等领域使用的模型密切相关。因此，该项目的结果将产生远远超出心理科学的影响。

The project will investigate two distinct but related questions in psychological research. The first concerns response time (RT), the time taken to complete an experimental task. The shape of the RT distribution serves as a key marker of cognitive processing. Research will develop statistical methodology for testing whether shape is invariant or depends on covariates such as participant characteristics and experimental manipulations. The approach will be to choose appropriate distributions from a large class of three parameter distributions derived from the two-parameter exponential families introduced by Bar-Lev and Reiser augmented with a shift parameter. A unified approach will develop objective Bayesian methodology for this class of nonregular distributions. The second key research question is about the association of latent mental processes across people, items, and conditions. Understanding how these processes are related will provide insight into understanding cognition. The specific problem is to model the association of covariance matrices of two or more related bivariate distributions in a hierarchical setting. The project will develop objective priors for Bayesian analysis of these covariance matrices, generalizing recent developments in univariate signal-to-noise ratio priors.Both phases of the project address fundamental and significant questions in cognitive research in psychology, with potential impact in related areas as well. The study of response times also is fundamental to research in developmental and social psychology as well as psychopathology. A number of theories have been developed for cognitive processing in these fields and how it is affected by experimental conditions and characteristics of the participant. Most of these theories predict shape changes in the distribution of response times. However, the fundamental question of whether or not the shape of these distributions actually changes as a response to experimental condition has not been studied. Understanding if and how response time distribution shape changes will spur new theoretical directions. In addition, useful new statistical methods will be developed applicable beyond psychology. The second problem, estimating covariance matrices of latent variables, is motivated by the study of different modes of recall in memory tasks. Participants given lists of words to study and subsequently queried on these words may respond because of an "automatic" response, based perhaps on previous familiarity, or they may respond based on actual recollection. Assessment of these two processes is complicated by the fact that some words may be simultaneously easier to recall automatically or easier to remember; similarly, people may tend to be better simultaneously at automatic response or recollection. Assessment of these relationships is delicate and challenging. The research will have impact on the psychological study of working memory and cognitive aging. In addition, the statistical models are closely related to those used in areas such as epidemiology, economics, and ecology. Thus the results of the project will have impact well beyond the psychological sciences.