Department of Biostatistics, Faculty of Medicine, Shiraz University of Medical Sciences, Shiraz, Iran.
Clinic for Neurology and Psychiatry for Children and Youth, Belgrade, Serbia.
Biomed Res Int. 2020 Feb 25;2020:1632350. doi: 10.1155/2020/1632350. eCollection 2020.
The logistic regression (LR) model for assessing differential item functioning (DIF) is highly dependent on the asymptotic sampling distributions. However, for rare events data, the maximum likelihood estimation method may be biased and the asymptotic distributions may not be reliable. In this study, the performance of the regular maximum likelihood (ML) estimation is compared with two bias correction methods including weighted logistic regression (WLR) and Firth's penalized maximum likelihood (PML) to assess DIF for imbalanced or rare events data. The power and type I error rate of the LR model for detecting DIF were investigated under different combinations of sample size, moderate and severe magnitudes of uniform DIF (DIF = 0.4 and 0.8), sample size ratio, number of items, and the imbalanced degree (). Indeed, as compared with WLR and for severe imbalanced degree ( = 0.069), there were reductions of approximately 30% and 24% under DIF = 0.4 and 27% and 23% under DIF = 0.8 in the power of the PML and ML, respectively. The present study revealed that the WLR outperforms both the ML and PML estimation methods when logistic regression is used to evaluate DIF for imbalanced or rare events data.
Logistic 回归（LR）模型在评估差异项目功能（DIF）方面高度依赖于渐近抽样分布。然而，对于稀有事件数据，最大似然估计方法可能存在偏差，渐近分布可能不可靠。本研究比较了常规最大似然（ML）估计与两种偏差校正方法，包括加权逻辑回归（WLR）和 Firth 惩罚最大似然（PML），以评估不平衡或稀有事件数据中的 DIF。研究了在不同样本量、中等和严重的均匀 DIF（DIF=0.4 和 0.8）、样本量比、项目数和不平衡程度（）组合下，LR 模型检测 DIF 的功效和Ⅰ型错误率。事实上，与 WLR 相比，对于严重的不平衡程度（=0.069），当 DIF=0.4 时，PML 和 ML 的功效分别降低了约 30%和 24%，当 DIF=0.8 时，PML 和 ML 的功效分别降低了 27%和 23%。本研究表明，当使用逻辑回归评估不平衡或稀有事件数据中的 DIF 时，WLR 优于 ML 和 PML 估计方法。
