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Latent variable sdelection in multidimensional item response theory models using the expectation model selection algorithm
British Journal of Mathematical and Statistical Psychology ( IF 2.6 ) Pub Date : 2021-12-17 , DOI: 10.1111/bmsp.12261
Ping-Feng Xu 1, 2 , Laixu Shang 2 , Qian-Zhen Zheng 2 , Na Shan 3 , Man-Lai Tang 4
Affiliation  

The aim of latent variable selection in multidimensional item response theory (MIRT) models is to identify latent traits probed by test items of a multidimensional test. In this paper the expectation model selection (EMS) algorithm proposed by Jiang et al. (2015) is applied to minimize the Bayesian information criterion (BIC) for latent variable selection in MIRT models with a known number of latent traits. Under mild assumptions, we prove the numerical convergence of the EMS algorithm for model selection by minimizing the BIC of observed data in the presence of missing data. For the identification of MIRT models, we assume that the variances of all latent traits are unity and each latent trait has an item that is only related to it. Under this identifiability assumption, the convergence of the EMS algorithm for latent variable selection in the multidimensional two-parameter logistic (M2PL) models can be verified. We give an efficient implementation of the EMS for the M2PL models. Simulation studies show that the EMS outperforms the EM-based L1 regularization in terms of correctly selected latent variables and computation time. The EMS algorithm is applied to a real data set related to the Eysenck Personality Questionnaire.

中文翻译:

使用期望模型选择算法的多维项目响应理论模型中的潜变量选择

多维项目响应理论(MIRT)模型中潜在变量选择的目的是识别多维测试的测试项目所探测的潜在特征。本文提出了Jiang等人提出的期望模型选择(EMS)算法。(2015)用于最小化具有已知潜在特征数量的 MIRT 模型中潜在变量选择的贝叶斯信息准则(BIC)。在温和的假设下,我们通过在存在缺失数据的情况下最小化观测数据的 BIC 来证明 EMS 算法在模型选择中的数值收敛性。对于 MIRT 模型的识别,我们假设所有潜在特征的方差是统一的,并且每个潜在特征都有一个仅与之相关的项目。在这种可识别性假设下,可以验证多维两参数逻辑 (M2PL) 模型中潜在变量选择的 EMS 算法的收敛性。我们为 M2PL 模型提供了 EMS 的有效实现。仿真研究表明,EMS 优于基于 EM 的根据正确选择的潜在变量和计算时间进行L 1正则化。EMS 算法应用于与 Eysenck Personality Questionnaire 相关的真实数据集。
更新日期:2021-12-17
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