Latent Variable Models in Action: Hierarchical Bayes and Mixture Models for Repeated Discrete Measures with Individual Differences

卡内基梅隆大学项目摘要：本研究的一个中心特征是开发广泛适用于教育、心理学和社会科学中测量问题的潜在变量模型的方法。这种方法正在几个特定领域得到发展和测试：从严格的单维潜在变量表示中得出的单调性和随机排序性质正在研究中，并应用于非参数标度问题。一种很有前途的马尔可夫链蒙特卡罗方法正在被推广并应用于各种问题，包括：正确建模成绩数据中的分数变异性；在多次重获人口普查中适应不同的可捕获性；开发离散重复测量的多维层次潜变量模型方法。此外，研究解决了推理对模型规格不足的敏感性。本研究的第二个重点是完善和发展现有的单维潜在结构的特征，使之成为一种评估潜在变量维数的统计理论和统计方法。这项工作旨在更充分地将心理测量和统计方法混合到重复离散测量的潜在变量模型中。心理测量学方法论倾向于关注模型构建和模型特征；心理测量数据分析倾向于尺度问题（选择“挂在一起”的问题，在单维潜在变量模型的意义上），可靠性（确保潜在变量可以从选择的问题中很好地估计出来），以及从数据中评估潜在变量的维度。统计方法倾向于回避这些基本的心理测量问题，而是专注于更精细的模型调整，以及各种推断和预测任务。本研究的重点是重复测量数据的潜在变量模型的统计和心理测量特征，这是定量心理学家，教育测量专家，认知科学家以及其他社会科学家感兴趣的。许多工作本质上是协作的，它是围绕理论和方法的发展而建立的，这些理论和方法的发展源于实质性的应用，并且对这些应用有用。--------------------------------------------------------------------------

NSF DMS-9705032 Latent variable models in action: hierarchical Bayes and mixture models for repeated discrete measures with individual differences Brian Junker Carnegie Mellon University PROJECT ABSTRACT: A central feature of this research is the development of widely applicable methodology for latent variable models for measurement problems in education, psychology and the social sciences. This methodology is being developed and tested in several specific areas: Monotonicity and stochastic ordering properties that follow from the strictly unidimensional latent variable representation are being studied and applied to nonparametric scaling problems. A promising Markov chain Monte Carlo method is being extended and applied to a variety of problems, including: correct modeling of rater variability in educational achievement data; accomodating heterogeneous catchability in multiple-recapture censuses; and developing methods for multidimensional and hierarchical latent variable models for discrete repeated measures. In addition, the research addresses the sensitivity of inferences to underspecification of the model. A second thrust of the research is to refine and develop existing characterizations of unidimensional latent structure into a statistical theory of, and statistical methods for assessing, latent variable dimensionality. This work aims to more fully blend psychometric and statistical approaches to latent variable models for repeated discrete measures. Psychometric methodology tends to concentrate on model building and model features; and psychometric data analysis tends toward issues of scaling (selecting questions that ``hang together'' in the sense that a unidimensional latent variable model holds), reliability (ensuring that the latent variable can be estimated well from the questions selected), and the assessment of latent variable dimensionality from data. Statistical methodology tends to sidestep these bas ic psychometric questions, and instead concentrates on finer model adjustments, and various inferential and predictive tasks. The focus of this research is on statistical and psychometric features of latent variable models for repeated measures data, which is of interest to quantitative psychologists, educational measurement specialists, and cognitive scientists, as well as other social scientists. Much of the work is collaborative in nature, and it is built around the development of theory and methodology motivated from, and useful for, substantive applications. --------------------------------------------------------------------------