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Measurement bias and error correction in a two-stage estimation for multilevel IRT models
British Journal of Mathematical and Statistical Psychology ( IF 2.6 ) Pub Date : 2021-02-07 , DOI: 10.1111/bmsp.12233
Xue Zhang 1 , Chun Wang 2
Affiliation  

Among current state-of-the-art estimation methods for multilevel IRT models, the two-stage divide-and-conquer strategy has practical advantages, such as clearer definition of factors, convenience for secondary data analysis, convenience for model calibration and fit evaluation, and avoidance of improper solutions. However, various studies have shown that, under the two-stage framework, ignoring measurement error in the dependent variable in stage II leads to incorrect statistical inferences. To this end, we proposed a novel method to correct both measurement bias and measurement error of latent trait estimates from stage I in the stage II estimation. In this paper, the HO-IRT model is considered as the measurement model, and a linear mixed effects model on overall (i.e., higher-order) abilities is considered as the structural model. The performance of the proposed correction method is illustrated and compared via a simulation study and a real data example using the National Educational Longitudinal Survey data (NELS 88). Results indicate that structural parameters can be recovered better after correcting measurement biases and errors.

中文翻译:

多级 IRT 模型两阶段估计中的测量偏差和误差校正

在目前最先进的多级IRT模型估计方法中,两阶段分治策略具有实际优势,如因子定义更清晰、便于二次数据分析、便于模型校准和拟合评估,并避免不正确的解决方案。然而,各种研究表明,在两阶段框架下,忽略第二阶段因变量的测量误差会导致统计推断不正确。为此,我们提出了一种新方法来纠正第二阶段估计中第一阶段潜在特征估计的测量偏差和测量误差。在本文中,HO-IRT模型被认为是测量模型,整体(即高阶)能力的线性混合效应模型被认为是结构模型。通过模拟研究和使用国家教育纵向调查数据 (NELS 88) 的真实数据示例,说明并比较了所提出的校正方法的性能。结果表明,在校正测量偏差和误差后,结构参数可以更好地恢复。
更新日期:2021-02-07
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