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：分层贝叶斯和混合 具有个体差异的重复离散测量模型 布莱恩·容克 卡内基梅隆大学 项目摘要： 这项研究的一个中心特点是广泛的发展， 潜在变量计量模型的适用方法 教育、心理学和社会科学中的问题。 这 正在几个具体领域制定和测试方法： 单调性和随机排序性质，从 严格一维潜变量表示正被 研究并应用于非参数标度问题。 一个有前途 马尔可夫链蒙特卡罗方法正在扩展和应用到一个 各种各样的问题，包括：评分员变异性的正确建模 在教育成就数据;适应异质性 多重再捕获普查的可捕获性;以及制定方法 对于多维和分层潜在变量模型， 离散的重复测量。 此外，研究还涉及 推断对模型规格不足的敏感性。 一 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化为一个 统计理论和统计方法评估，潜在的， 可变维度。 这项工作旨在更充分地融合心理测量和统计 重复离散测量的潜变量模型方法。 心理测量学方法倾向于集中于模型的建立， 模型特征;心理测量数据分析倾向于以下问题： 缩放（选择“挂在一起”的问题， 一维潜变量模型保持）、可靠性（确保 潜变量可以很好地从问题中估计出来 选择），以及潜在变量维度的评估， 数据 统计方法往往会避开这些基本原则。 心理测量问题，而是专注于更精细的模型 调整，以及各种推理和预测任务。 重点 本研究的主要目的是研究潜在的心理特征， 重复测量数据的变量模型，这是感兴趣的， 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。 大部分 工作本质上是协作的，它是围绕着 发展理论和方法，其动机是， 实质性应用。 --------------------------------------------------------------------------

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