組內相關係數與樣本數對於脈絡效果估計的影響：貝氏估計與最大概似估計法的比較

Abstract

在多層次模式中，脈絡效果被定義為脈絡變數（個體層次解釋變數的組平均）對於結果變數的影響在排除了個體層次解釋變數的影響後的淨效果，脈絡效果在教育與心理領域用來反映個體所身存的情境對個體所造成的影響，不僅具有方法學上的重要分析價值，更有教育與心理研究之理論與議題意涵。本研究針對解釋變數與結果變數的組內相關係數配對效果，配合樣本數的不同狀況，進行蒙地卡羅模擬研究，並以來自於38家企業1,200名員工的組織創新氣氛與滿意度測量數據進行實徵資料分析。在分析時，本研究特別導入貝氏估計進行模擬研究與實徵資料的各係數與脈絡效果的參數估計，並與最大概似估計進行比較。從模擬研究的分析結果發現，在樣本愈小的情況下，ICCx愈大而ICCy愈小，對於脈絡效果的真值估計愈精確。相對之下，ICCx愈小而ICCy愈大時，參數波動愈大而真值偏誤愈嚴重。同時，模擬結果也發現貝氏估計與ML估計的效率相當一致，而貝氏估計在各種模擬條件下對於脈絡效果真值估計的表現普遍優於最大概似估計。尤其在Ncluster偏低的情況下，貝氏估計有更優越的效能，顯示貝氏估計是最大概似法的良好替代。在實徵分析部分，本研究也發現貝氏估計能夠由蒙地卡羅模擬估計過程中得知誤差發生情形，對於脈絡效果的估計與解釋具有實質助益。最後，本研究對於未來研究建議與研究限制進行討論。

In multilevel modeling, contextual effects are defined as the pure effects of contextual variables on the outcomes after the impact of explanative variable at individual level been removed. The multilevel model with contextual effect is frequently of interest in education and psychological research since the group means of the explanative variable at individual level reflected the situational influence have both methodological an substantive meanings. In the present study, a Monte Carlo simulation along with an empirical data contained 38 companies and 1,200 employees are adapted to explore the influences of intra-class correlation (ICC) of predictor and outcome on the estimation of contextual effects. The Bayesian estimation was applied in this present study in order to compare with the traditional maximum likelihood method. Results of simulation study revealed that, in the cases of small sample size, a smaller ICCx combined with a higher ICCy has better efficient for the parameter estimation; in contrast, a higher ICCx combined with a lower ICCy may has poor performance. The performance of Bayesian estimation is similar with maximum likelihood method. However, the Bayesian estimation shown the superiority of predicting the true value of parameter especially when the Ncluster is low, revealing that the Bayesian estimates is the good alternative with the maximum likelihood method for estimating the contextual effects in the multilevel models. Finally, the limitations and future study are discussed in the end of the paper.