Doctoral Dissertation Research: A Metropolis-Hastings Robbins-Monro Algorithm for Maximum Likelihood Confirmatory Item Factor Analysis

博士论文研究：最大似然验证项因子分析的 Metropolis-Hastings Robbins-Monro 算法

• 批准号: 0717941
• 负责人: Robert MacCallum
• 金额: $ 0.7万
• 依托单位: University of North Carolina at Chapel Hill
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-09-01 至 2008-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0717941&HistoricalAwards=false
• 关键词: Doctoral; Dissertation; Research; Metropolis; Hastings

Confirmatory item factor analysis (IFA) has seen increasing use in the social, behavioral, and health sciences. IFA allows a researcher to specify models that hypothesize the factor structure of a battery of test items, e.g., standardized educational assessments, personality inventories, and patient reported quality of life measures. However, the maximum marginal likelihood (MML) approach to parameter estimation in IFA presents difficult numerical integration problems that challenge existing approaches of estimation. The project will study a new parameter estimation algorithm for confirmatory IFA that combines the Metropolis-Hastings sampler and the Robbins-Monro stochastic approximation algorithm. The new algorithm is called the Metropolis-Hastings Robbins-Monro (MH-RM) algorithm. The project will further integrate existing research on algorithms for multidimensional IFA, extend MH-RM to ordinal and nominal item types, explore the merits of different implementations of MH-RM, and examine methods of convergence acceleration. The project will evaluate the performance of the new algorithm by means of simulations and comparisons with current "gold standard" algorithms using real and simulated item response data. The project also will investigate the possibility of taking advantage of inherent features of MH-RM in modern parallel processing computing environments.The MH-RM algorithm has the potential of becoming the first general and self-adaptive algorithm for arbitrarily high-dimensional IFA. It naturally integrates existing research on IFA and furthers the understanding of the relationship between latent trait models and incomplete data estimation. The project will develop a viable method for evaluating the factor structure of test items, solve problems with current estimation algorithms, and enhance the development of modern test theory. The project is likely to have an impact on any field that uses IFA as a data analytic tool. As a result, the project will aid in enhancing the quality of tests and the research that uses those tests in the educational, psychological, and health outcomes related fields. As a Doctoral Dissertation Research Improvement award, this award also will provide support to enable a promising student to establish a strong independent research career.

验证性项目因子分析（IFA）在社会科学、行为科学和健康科学中的应用越来越广泛。IFA允许研究人员指定模型，假设一系列测试项目的因素结构，例如，标准化教育评估，个性清单和患者报告的生活质量测量。然而，最大边际似然（MML）方法在IFA参数估计中提出了困难的数值积分问题，对现有的估计方法提出了挑战。该项目将研究一种新的验证性IFA参数估计算法，该算法结合了Metropolis-Hastings采样器和Robbins-Monro随机逼近算法。该算法被称为Metropolis-Hastings Robbins-Monro （MH-RM）算法。该项目将进一步整合现有的多维IFA算法研究，将MH-RM扩展到有序和标称项目类型，探索不同MH-RM实现的优点，并研究收敛加速方法。该项目将利用真实和模拟的项目响应数据，通过模拟和与当前“黄金标准”算法的比较来评估新算法的性能。该项目还将研究在现代并行处理计算环境中利用MH-RM固有特性的可能性。MH-RM算法有可能成为第一个适用于任意高维IFA的通用自适应算法。它自然地整合了现有的IFA研究，并进一步理解了潜在性状模型与不完全数据估计之间的关系。该项目将开发一种可行的评估测试项目因素结构的方法，解决现有估计算法的问题，促进现代测试理论的发展。该项目可能会对任何使用IFA作为数据分析工具的领域产生影响。因此，该项目将有助于提高测试的质量和在教育、心理和健康结果相关领域使用这些测试的研究。作为博士论文研究改进奖，该奖项还将提供支持，使有前途的学生建立一个强大的独立研究生涯。