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

验证性项目因素分析(IFA)在社会、行为和健康科学中的应用越来越广泛。IFA允许研究人员指定假设一系列测试项目的因素结构的模型，例如标准化的教育评估、个性问卷和患者报告的生活质量测量。然而，IFA中参数估计的最大边际似然(MML)方法存在困难的数值积分问题，这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。新算法称为Metropolis-Hastings Robbins-Monro(MH-RM)算法。该项目将进一步整合已有的多维IFA算法研究，将MH-RM扩展到序项和名义项类型，探索MH-RM不同实现的优点，并研究收敛加速的方法。该项目将通过使用真实和模拟的项目响应数据进行模拟并与当前的“黄金标准”算法进行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算法固有特性的可能性。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特质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方法来评估测试项目的因素结构，解决现有估计算法存在的问题，并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，以及在教育、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。

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.