Theory and Applications of Latent Variable and Mixture Models for Repeated Measurements

重复测量潜变量和混合模型的理论与应用

• 批准号: 9404438
• 负责人: Brian Junker
• 金额: $ 7.5万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9404438&HistoricalAwards=false
• 关键词: Theory; Applications; Latent; Variable; Mixture

The focus of this work is on strictly unidimensional latent variable models, which may be thought of as mixture models which induce conditional association (Rosenbaum, 1984; Holland and Rosenbaum, 1986) in the marginal distribution of the data, or as a special case of Stout's (1987, 1990) essentially unidimensional models. I propose to extend my past efforts to use these ideas together with notions from the literature on positive and negative dependence (e.g. Joag-Dev, 1983; Joag-Dev and Proschan, 1982; Newman and Wright, 1981; or more recently the collection edited by Block, Sampson and Savits, 1990) to characterize strictly unidimensional models. My recent explorations of this problem suggest a reasonably straightforward approach that, as a side benefit, generalizes de Finetti's characterization of exchangeability, without the need to specify sufficient statistics as in, for example, Diaconis and Freedman (1984). A second line of work in this proposal is the exploration, using asymptotic methods along the lines of Kass, Tierney and Kadane (1990), and Clarke and Barron (1990), of inferences about the latent trait under a strictly unidimensional model, which asserts conditional independence given the latent trait, when in fact some mild form of conditional dependence holds. In addition, biases in the asymptotic standard error of an MLE-like estimator can also be calculated and, in some cases, corrected using nonparametric regression ideas due to Ramsay (Ramsay, 1991; Ramsay and Winsburg, 1991). Finally, some problems in applications and computing will be examined, including unifying and extending nonparametric techniques for latent variables data analysis (e.g. Molenaar, 1991; and Grayson, 1988); and developing parametric statistical models and computational methods (e.g. efficient estimation of a polytomous version of the model specified by Lindsay, Clogg and Grego, 1991) that arise in the analysis of data from small scale experiments in cognitive science. This proposal concerns statistical and probabilistic features of latent variable models for repeated measures data, which is of interest to quantitative psychologists, psychometricians, and cognitive scientists, as well as other social scientists. A typical application for latent variable models is psychological measurement, in which the latent variable is an unobservable variable that indicates the level of a psychological feature of a person---such as depression, mathematical aptitude, job satisfaction, or working memory capacity---that we observe only indirectly through the person's responses to a series of tasks, questionnaire items, etc. Data of this type might be obtained from psychiatric rating forms, standardized academic achievement or aptitude tests like the SAT and GRE, standardized questionnaires in sociology, or coded responses to a set of tasks in experiments in cognitive psychology. A primary outcome of this research will be a deeper understanding of latent variable models for measurement problems, at both the level of fundamental statistical theory and the level of practical applications. Practical tools arising from this research would include: enhanced methods for deciding how well or poorly this class of models matches particular situations or data sets; rules for adjusting scientific inferences based on these models for the inevitable mismatch, however small, between the model being used and the mechanism that generated the data; and computational and model-building methods that are adapted to small-scale experimental data, such as might be found in cognitive psychology, where these models are conceptually natural but current methods tend to break down. Much of the work proposed here is built around interdisciplinary collaboration, especially with quantitative psychologists and educational measurement specialists, with the goal of developing statistical theory that will be of use in applications.

这项工作的重点是严格的一维潜变量模型，它可以被认为是在数据的边际分布中诱导条件关联的混合模型（Rosenbaum，1984；Holland 和 Rosenbaum，1986），或者作为 Stout（1987，1990）本质上一维模型的特例。我建议扩展我过去的努力，将这些想法与积极和消极依赖文献中的概念（例如 Joag-Dev，1983 年；Joag-Dev 和 Proschan，1982 年；Newman 和 Wright，1981 年；或者最近由 Block、Sampson 和 Savits，1990 年编辑的合集）一起使用，以表征严格的一维模型。我最近对这个问题的探索提出了一种相当简单的方法，作为一个附带好处，概括了德菲内蒂对可交换性的描述，而不需要像 Diaconis 和 Freedman (1984) 那样指定足够的统计数据。该提案的第二个工作是使用 Kass、Tierney 和 Kadane (1990) 以及 Clarke 和 Barron (1990) 的渐近方法，在严格的一维模型下对潜在特征进行推断，该模型断言给定潜在特征的条件独立性，而实际上存在某种温和形式的条件依赖性。此外，还可以计算类 MLE 估计量的渐近标准误差中的偏差，并且在某些情况下，可以使用 Ramsay 提出的非参数回归思想进行纠正（Ramsay，1991；Ramsay 和 Winsburg，1991）。最后，将研究应用和计算中的一些问题，包括统一和扩展潜在变量数据分析的非参数技术（例如 Molenaar，1991；和 Grayson，1988）；开发参数统计模型和计算方法（例如 Lindsay、Clogg 和 Grego，1991 指定的模型的多部分版本的有效估计），这些模型和计算方法出现在认知科学小规模实验的数据分析中。 该提案涉及重复测量数据的潜变量模型的统计和概率特征，这引起了定量心理学家、心理测量学家、认知科学家以及其他社会科学家的兴趣。潜变量模型的典型应用是心理测量，其中潜变量是一种不可观察的变量，它表明一个人的心理特征水平，例如抑郁、数学能力、工作满意度或工作记忆能力，我们只能通过人对一系列任务、问卷项目等的反应来间接观察到这些特征。此类数据可以从精神病学评级表、标准化学术报告中获得。 SAT 和 GRE 等成就或能力测试、社会学标准化问卷或认知心理学实验中对一组任务的编码反应。这项研究的主要成果将是在基础统计理论和实际应用层面上更深入地理解测量问题的潜在变量模型。 这项研究产生的实用工具包括： 用于确定此类模型与特定情况或数据集的匹配程度的增强方法；用于调整基于这些模型的科学推论的规则，以应对所使用的模型和生成数据的机制之间不可避免的不匹配（无论多么小）；以及适应小规模实验数据的计算和模型构建方法，例如认知心理学中可能发现的方法，其中这些模型在概念上是自然的，但当前的方法往往会崩溃。这里提出的大部分工作都是围绕跨学科合作建立的，特别是与定量心理学家和教育测量专家的合作，其目标是发展可在应用中使用的统计理论。