改进多维项目反应理论的变分估计。

IF 2.9 2区 心理学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Psychometrika Pub Date : 2024-03-01 Epub Date: 2023-11-18 DOI:10.1007/s11336-023-09939-0
Chenchen Ma, Jing Ouyang, Chun Wang, Gongjun Xu
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引用次数: 0

摘要

社会科学的许多领域经常使用调查工具和评估。当这些评估试图测量的结构变得多方面时,多维项目反应理论(MIRT)为项目分析、校准和评分提供了一个统一的框架和方便的统计工具。然而,估计MIRT模型的计算挑战阻碍了它的广泛使用,因为当维度数量、样本量和测试长度很大时,许多现有的方法很难在现实的时间框架内提供结果。相反,变分估计方法,如高斯变分期望最大化(GVEM)算法,最近被提出,通过提供快速和准确的解决方案来解决估计挑战。然而,结果表明,变分估计方法在验证性模型估计中可能会对判别参数产生一定的偏差,本文提出了一个重要加权版的GVEM(即IW-GVEM)来纠正MIRT模型下的这种偏差。我们还使用自适应矩估计方法来自动更新梯度下降的学习率。仿真结果表明,与GVEM相比,IW-GVEM可以在不增加计算时间的情况下有效地校正偏置。该方法对其他心理测量模型的变分估计也有一定的借鉴意义。
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A Note on Improving Variational Estimation for Multidimensional Item Response Theory.

Survey instruments and assessments are frequently used in many domains of social science. When the constructs that these assessments try to measure become multifaceted, multidimensional item response theory (MIRT) provides a unified framework and convenient statistical tool for item analysis, calibration, and scoring. However, the computational challenge of estimating MIRT models prohibits its wide use because many of the extant methods can hardly provide results in a realistic time frame when the number of dimensions, sample size, and test length are large. Instead, variational estimation methods, such as Gaussian variational expectation-maximization (GVEM) algorithm, have been recently proposed to solve the estimation challenge by providing a fast and accurate solution. However, results have shown that variational estimation methods may produce some bias on discrimination parameters during confirmatory model estimation, and this note proposes an importance-weighted version of GVEM (i.e., IW-GVEM) to correct for such bias under MIRT models. We also use the adaptive moment estimation method to update the learning rate for gradient descent automatically. Our simulations show that IW-GVEM can effectively correct bias with modest increase of computation time, compared with GVEM. The proposed method may also shed light on improving the variational estimation for other psychometrics models.

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来源期刊
Psychometrika
Psychometrika 数学-数学跨学科应用
CiteScore
4.40
自引率
10.00%
发文量
72
审稿时长
>12 weeks
期刊介绍: The journal Psychometrika is devoted to the advancement of theory and methodology for behavioral data in psychology, education and the social and behavioral sciences generally. Its coverage is offered in two sections: Theory and Methods (T& M), and Application Reviews and Case Studies (ARCS). T&M articles present original research and reviews on the development of quantitative models, statistical methods, and mathematical techniques for evaluating data from psychology, the social and behavioral sciences and related fields. Application Reviews can be integrative, drawing together disparate methodologies for applications, or comparative and evaluative, discussing advantages and disadvantages of one or more methodologies in applications. Case Studies highlight methodology that deepens understanding of substantive phenomena through more informative data analysis, or more elegant data description.
期刊最新文献
Rejoinder to McNeish and Mislevy: What Does Psychological Measurement Require? Are Sum Scores a Great Accomplishment of Psychometrics or Intuitive Test Theory? Correction to: Generalized Structured Component Analysis Accommodating Convex Components: A Knowledge-Based Multivariate Method with Interpretable Composite Indexes. Variational Estimation for Multidimensional Generalized Partial Credit Model. Proof of Reliability Convergence to 1 at Rate of Spearman-Brown Formula for Random Test Forms and Irrespective of Item Pool Dimensionality.
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