納入背景變項對群體參數估計之影響的模擬與實徵研究

A Simulation and Empirical Study on Incorporating Background Variables in Population Parameters Estimation

大型測驗（NAEP、TIMSS和PISA)是透過「可能值方法」了解母群的學習成效 或不同背景造成的影響。可能值方法是以潛在迴歸模式，加入學生背景變項計算後驗 分布，並抽取可能值，以利於次級資料分析者使用。本研究分別使用模擬與實徵資 料，探討常用的點估計方法以及使用可能值方法對於群體參數估計的影響，並探討不 同相關程度的背景變項對於群體參數估計之成效，以及不同模式下群體參數回復性。\r研究結果顯示，最大概似估計法（MLE)、期望後驗法（EAP)，以及可能值 (PV)等三種方法，在回復群體平均數時，三種方法並無太大的差異，但在回復 群體變異數時，使用可能值（PV)的方法有較好的回復性。此外，當背景變項以 原始資料形式納入，或利用主成分分析進行轉換後納入潛在迴歸模式中，這兩者模 式對於群體參數回復性並無太大差異，顯示利用主成分進行轉換的背景變項也可以 達到與原始資料形式納入相同的效果。當所欲探討的背景變項群體參數被納入潛在 迴歸模式中，則對於此背景變項群體參數有較佳的回復性，舉例來説：欲探討「性 別」這個背景變項的群體參數時，則當「性別」這個背景變項被納入潛在迴歸模式 中，會有較佳的回復性，且當所納入的背景變項與能力值間的相關程度較高時，對 於背景變項群體參數的估計值有較好的回復性。

In the large-scale assessment programs such as NAEP， TIMSS and PISA use plausible value (PV) method to estimate the population statistics and to explore the effects upon the achievement of the different background variables such as gender. In the plausible value method， the background variables of examinees are incorporated into the latent regression model to estimate the posterior distributions ofthe abilities. Plausible values that provided for secondary analysts are random draws from the posterior distributions. In this paper， the performances on estimating population statistics between plausible value method and traditional IRT ability estimations (ex. MLE or EAP) are evaluated. The influences of the different correlation degrees between background variables and abilities and different regression models on estimating population statistics are also explored.The results show that the mean of population ability is estimated well whether MLE， EAP or PV is used. The PV has the best performance on recovering the variance of population ability. Two models， principle component analysis are applied to compress most of the background variables and raw background variables forms， have the same performances on recovery of population statistics. If there is an interest in estimating for specific sub-groups (ex. Gender)， the incorporation of the related background variables get better recoveries on the statistics of these sub-groups. The higher correlation between background variables and abilities can lead to increased precision ofpopu-lation statistics.