Zhu Hongyue, Gao Wei, Zhang Xue
School of Mathematics and Statistics, Northeast Normal University, Changchun, China.
China Institute of Rural Education Development, Northeast Normal University, Changchun, China.
Front Psychol. 2021 Jan 8;11:607731. doi: 10.3389/fpsyg.2020.607731. eCollection 2020.
Multilevel item response theory (MLIRT) models are used widely in educational and psychological research. This type of modeling has two or more levels, including an item response theory model as the measurement part and a linear-regression model as the structural part, the aim being to investigate the relation between explanatory variables and latent variables. However, the linear-regression structural model focuses on the relation between explanatory variables and latent variables, which is only from the perspective of the average tendency. When we need to explore the relationship between variables at various locations along the response distribution, quantile regression is more appropriate. To this end, a quantile-regression-type structural model named as the quantile MLIRT (Q-MLIRT) model is introduced under the MLIRT framework. The parameters of the proposed model are estimated using the Gibbs sampling algorithm, and comparison with the original (i.e., linear-regression-type) MLIRT model is conducted via a simulation study. The results show that the parameters of the Q-MLIRT model could be recovered well under different quantiles. Finally, a subset of data from PISA 2018 is analyzed to illustrate the application of the proposed model.
多级项目反应理论（MLIRT）模型在教育和心理学研究中被广泛应用。这种类型的建模有两个或更多层次，包括作为测量部分的项目反应理论模型和作为结构部分的线性回归模型，目的是研究解释变量与潜在变量之间的关系。然而，线性回归结构模型关注的是解释变量与潜在变量之间的关系，这仅仅是从平均趋势的角度。当我们需要探索沿反应分布不同位置的变量之间的关系时，分位数回归更为合适。为此，在MLIRT框架下引入了一种名为分位数MLIRT（Q-MLIRT）模型的分位数回归型结构模型。使用吉布斯采样算法估计所提出模型的参数，并通过模拟研究与原始（即线性回归型）MLIRT模型进行比较。结果表明，Q-MLIRT模型的参数在不同分位数下都能很好地恢复。最后，对2018年国际学生评估项目（PISA）的一部分数据进行分析，以说明所提出模型的应用。
