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

NSF DMS-9705032潜变量模型的作用：具有个体差异的重复离散测量的分层贝叶斯和混合模型布赖恩·容克·卡内基梅隆大学项目摘要：这项研究的一个中心特征是为教育、心理学和社会科学中测量问题的潜变量模型发展了广泛适用的方法学。这种方法正在几个特定的领域得到开发和测试：严格一维潜变量表示的单调性和随机序性质正在被研究并应用于非参数尺度问题。一种很有前途的马尔可夫链蒙特卡罗方法正在被扩展并应用于各种问题，包括：在教育成就数据中对评分者变异性的正确建模；在多次重新捕获人口普查中适应不同类型的可捕性；以及为离散重复测量开发多维和分层潜变量模型的方法。此外，本研究还探讨了推论对模型说明不足的敏感性。研究的第二个重点是改进和发展现有的一维潜在结构的特征，成为潜在变量维度的统计理论和评估的统计方法。这项工作旨在更全面地将心理测量学和统计学方法融合到重复离散测量的潜变量模型中。心理测量学方法倾向于集中于模型建立和模型特征；心理测量学数据分析倾向于尺度(从一维潜变量模型的意义上选择“结合在一起的”问题)、可靠性(确保可以从所选问题中很好地估计潜在变量)以及从数据中评估潜在变量维度的问题。统计学方法倾向于回避这些基本的心理测量学问题，转而专注于更精细的模型调整，以及各种推理和预测任务。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学特征，这是定量心理学家、教育测量专家、认知科学家和其他社会科学家感兴趣的。许多工作本质上是协作的，它是围绕以实质性应用为动机并对其有用的理论和方法的发展而建立的。------------------------

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. --------------------------------------------------------------------------