{"title":"A unified EM framework for estimation and inference of normal ogive item response models.","authors":"Xiangbin Meng, Gongjun Xu","doi":"10.1111/bmsp.12356","DOIUrl":null,"url":null,"abstract":"<p><p>Normal ogive (NO) models have contributed substantially to the advancement of item response theory (IRT) and have become popular educational and psychological measurement models. However, estimating NO models remains computationally challenging. The purpose of this paper is to propose an efficient and reliable computational method for fitting NO models. Specifically, we introduce a novel and unified expectation-maximization (EM) algorithm for estimating NO models, including two-parameter, three-parameter, and four-parameter NO models. A key improvement in our EM algorithm lies in augmenting the NO model to be a complete data model within the exponential family, thereby substantially streamlining the implementation of the EM iteration and avoiding the numerical optimization computation in the M-step. Additionally, we propose a two-step expectation procedure for implementing the E-step, which reduces the dimensionality of the integration and effectively enables numerical integration. Moreover, we develop a computing procedure for estimating the standard errors (SEs) of the estimated parameters. Simulation results demonstrate the superior performance of our algorithm in terms of its recovery accuracy, robustness, and computational efficiency. To further validate our methods, we apply them to real data from the Programme for International Student Assessment (PISA). The results affirm the reliability of the parameter estimates obtained using our method.</p>","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":1.5000,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"British Journal of Mathematical & Statistical Psychology","FirstCategoryId":"102","ListUrlMain":"https://doi.org/10.1111/bmsp.12356","RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
Normal ogive (NO) models have contributed substantially to the advancement of item response theory (IRT) and have become popular educational and psychological measurement models. However, estimating NO models remains computationally challenging. The purpose of this paper is to propose an efficient and reliable computational method for fitting NO models. Specifically, we introduce a novel and unified expectation-maximization (EM) algorithm for estimating NO models, including two-parameter, three-parameter, and four-parameter NO models. A key improvement in our EM algorithm lies in augmenting the NO model to be a complete data model within the exponential family, thereby substantially streamlining the implementation of the EM iteration and avoiding the numerical optimization computation in the M-step. Additionally, we propose a two-step expectation procedure for implementing the E-step, which reduces the dimensionality of the integration and effectively enables numerical integration. Moreover, we develop a computing procedure for estimating the standard errors (SEs) of the estimated parameters. Simulation results demonstrate the superior performance of our algorithm in terms of its recovery accuracy, robustness, and computational efficiency. To further validate our methods, we apply them to real data from the Programme for International Student Assessment (PISA). The results affirm the reliability of the parameter estimates obtained using our method.
正态椭圆(NO)模型为项目反应理论(IRT)的发展做出了巨大贡献,并已成为流行的教育和心理测量模型。然而,NO 模型的估计在计算上仍然具有挑战性。本文旨在提出一种高效可靠的拟合 NO 模型的计算方法。具体来说,我们引入了一种新颖、统一的期望最大化(EM)算法,用于估计 NO 模型,包括双参数、三参数和四参数 NO 模型。我们的 EM 算法的一个关键改进在于将 NO 模型增强为指数族中的一个完整数据模型,从而大大简化了 EM 迭代的实现,并避免了 M 步中的数值优化计算。此外,我们还提出了实施 E 步的两步期望程序,从而降低了积分的维度,并有效地实现了数值积分。此外,我们还开发了一种用于估计估计参数标准误差(SE)的计算程序。仿真结果表明,我们的算法在恢复精度、稳健性和计算效率等方面都表现出色。为了进一步验证我们的方法,我们将其应用于国际学生评估项目(PISA)的真实数据。结果肯定了使用我们的方法获得的参数估计的可靠性。
期刊介绍:
The British Journal of Mathematical and Statistical Psychology publishes articles relating to areas of psychology which have a greater mathematical or statistical aspect of their argument than is usually acceptable to other journals including:
• mathematical psychology
• statistics
• psychometrics
• decision making
• psychophysics
• classification
• relevant areas of mathematics, computing and computer software
These include articles that address substantitive psychological issues or that develop and extend techniques useful to psychologists. New models for psychological processes, new approaches to existing data, critiques of existing models and improved algorithms for estimating the parameters of a model are examples of articles which may be favoured.