Nonparametric Mixture Models

虽然许多个体差异对普通的观察者来说是显而易见的--例如，身高、体重、发色或肤色的差异--但从行为科学的角度来看，可以说更重要的个体差异是潜在的，没有被观察到。这个项目将开发统计方法，将给定的总体划分为不同的成分分布，包括估计成分的数量和非参数估计成分分布。这些不同的成分反映了种群中潜在的个体差异。这项研究与其他关于混合模型的研究的一个主要不同之处在于，该研究的重点是削弱通常很强且可能不现实的参数假设，这些假设在过去可能限制了混合理论的更广泛应用。具体地说，这项研究将比较现有的贝叶斯方法来确定非参数混合物中的组份数量，并开发新的贝叶斯方法。当协变量信息可用时，该项目将研究回归的混合，其中的目标是估计作为协变量的函数的混合比例(S)。最后，该项目将使用分析和计算机模拟方法，将以前资助的非参数混合模型研究扩展到单向布局和多重比较，这是一个传统方法，如方差分析和标准非参数替代方法，无法检测到某些类型的组差异。在这个项目中开发的混合模型使得概念化和识别个体的潜在差异成为可能，例如思维方式的差异。这些组合不仅提供了一个有用的概念视角，而且也提供了一个实践视角，因为它可以在个人层面上确定一个人在解决问题时最有可能使用的认知策略(例如)。有了一个框架来概念化和确定成长中的儿童在那些对有效学习和学业成绩至关重要的潜在(未观察到)过程中的不同之处，将对如何构建学习环境产生重要影响。然而，开发的技术主要是出于心理考虑，适用于任何使用统计数据分析的科学实证调查领域，在这些领域中，潜在变量具有可测量的影响。因此，这项研究对各种智力活动具有广泛的影响。

While many individual human differences are obvious to the casual observer - differences in height, weight, hair color or complexion, for example - arguably the more important individual differences, from a behavioral science perspective, are latent and not observed. This project will develop statistical methods for separating a given population into its distinct component distributions, including estimation of the number of components and nonparametric estimation of the component distributions. These different components reflect the latent individual differences in the population. A principal way in which this research differs from other research on mixture models is that the focus is on weakening the often strong and possibly unrealistic parametric assumptions that have, in the past, possibly limited the wider application of mixture theory. Specifically, this research will compare existing Bayesian methods to determine the number of components in a nonparametric mixture and develop new Bayesian methods. When covariate information is available, the project will study mixtures of regressions, in which a goal is the estimation of the mixing proportions as a function of the covariate(s). Finally, the project will use analytical and computer simulation methods to expand previously funded research in nonparametric mixture models to the one-way layout and multiple comparisons, an area in which traditional methods such as analysis of variance and standard nonparametric alternatives can fail to detect certain kinds of group differences. The mixture models developed in this project make it possible to both conceptualize and identify individual latent differences such as differences in thinking styles. These mixtures provide not only a useful conceptual perspective but a practical one as well, in that it is possible to identify, at the level of the individual, which cognitive strategy (for example) a person most likely used in the solution of a problem. Having a framework for conceptualizing and identifying how growing children are different in those latent (unobserved) processes vital for effective learning and school achievement would have important implications for how learning environments are constructed. Yet the techniques developed, largely motivated by psychological concerns, are applicable to any field of scientific empirical inquiry employing statistical data analysis in which latent variables have a measurable impact. Thus, this research has broad implications for a variety of intellectual activities.