探討差異試題功能檢核中的遺漏變數偏誤

Omitted Variable Bias in Differential Item Functioning Assessment

差異試題功能（differential item functioning, DIF）檢核已廣泛於試題分析中進行以確保測驗公平性；然而，少有研究考量遺漏變數偏誤（omitted variable bias, OVB）對DIF檢核的影響。忽略OVB可能會影響參數估計值的不偏性，並導致DIF檢核之型一誤差膨脹與檢定力下降。測驗實務者可能因此錯誤判斷組別變項出現不公平現象，並據此錯誤訊息進行DIF試題修改。為改善此問題，本研究針對兩議題進行探討。第一、評估原始DIF檢核法（DIF檢核時不考慮混淆變項）對於OVB之強韌性，亦即評估忽略OVB對DIF檢核造成的影響。第二、加入向後量尺淨化程序（backward scale purification, BSP）以提升控制法（DIF檢核時納入所有混淆變項）的DIF檢核成效，解決該方法在估計偏誤與檢核無效率上的兩難。據此，本研究進行三個模擬研究。研究一評估DIF檢核時之型一誤差。結果顯示控制法能有效控管型一誤差；但原始法在混淆變項具DIF且分組變項間存在高相關時，會出現型一誤差失控的情形。研究二評估DIF檢核時之型二誤差。結果顯示當混淆變項數量降低且組別變項間相關增加時，控制法之型二誤差會出現膨脹情形。研究三在控制法中加入BSP以降低型二誤差。研究結果顯示，BSP能有效控制型一誤差，並維持良好檢定力。總結而言，BSP應能有效幫助測驗實務者在DIF檢核中處理OVB，確保測驗公平性與效度。

Differential item functioning (DIF) assessment has been widely applied for decades to ensure test fairness in routine item analysis. However, few studies have investigated, or even noticed, omitted variable bias (OVB) while assessing DIF. As a result, the estimation of DIF effects may not be unbiased, resulting in inflated type I error rates and/or deflated power rates of DIF assessment. In testing practices, test practitioners may, therefore, wrongly identify inequality among grouping variables and revise the flagged DIF items based on misleading information. To overcome these problems, two issues were addressed in detail in this study. The first issue is the robustness of the original method (i.e., assessing DIF without considering confounding variables) to OVB, which was examined by evaluating the impact of ignoring OVB in DIF assessment. The second issue occurs when the controlled method (i.e., including all grouping variables) encounters the so-called trade-off between bias and inefficiency while assessing DIF. To address this issue, the backward scale purification (BSP) procedure was applied to the controlled method to improve the performance of DIF assessment. Accordingly, three interrelated studies were conducted. In Study 1, type I error rates for the original and controlled methods in DIF assessment were investigated. The results indicated that the controlled method can well control type I error rates under all conditions. In contrast, the original method lost control of type I error rates when confounding variables exhibited DIF and the correlation among grouping variables was high (i.e., greater than or equal to .2). In Study 2, type II error rates of the controlled method were investigated. In comparison to the true model, the results indicated that the type II error rates of the controlled method increased as the number of confounding variables decreased and the correlation among grouping variables increased. This result manifests the trade-off between bias and inefficiency when adding additional variables to the model. In Study 3, the BSP was applied to the controlled method to reduce the type II error rates. The results indicated that BSP can effectively control type I error rates while maintaining acceptable power rates. In summary, the controlled method with BSP appears promising for helping test practitioners deal with OVB in DIF assessment, thereby ensuring fairness and validity in testing practices.