階層線性模式與一般線性迴歸模式檢定力的比較

Power Comparison of Hierarchical Linear Model and Ordinary Linear Regression

簡嘉惠(CHIA-HUI CHIEN)

指導教授 ： 施葦

國立臺北大學/商學院/統計學系/碩士(2010年)

摘要

階層性資料是指低階的個體資料會受到高階的群組特性影響，構成在相同高階層次的個體間存在高度相關。階層線性模式(Hierarchical Linear Model, HLM)是一種將迴歸模型擴展到具有階層結構資料上的統計分析方法。
本研究旨在比較探討當研究者正確使用階層線性模式於嵌套性資料上，與忽略資料的相關性問題而沿用一般線性迴歸(Ordinary Linear Regression)模型，所造成統計推論的影響。經由模擬的方式，變動資料的組內相關係數(Intraclass Correlation Coefficient, ICC)以及樣本數，針對檢定低階解釋變數的固定效果，比較階層模型與一般線性迴歸模型在型一誤機率與檢定力的表現狀況。
透過模擬的結果發現，隨著資料的相依程度增加，一般線性迴歸的型一誤機率愈加無法維持在所設定的型一誤水準。在兩模型之型一誤機率具有穩定表現時，一般線性迴歸模型檢定力與階層線性模型在不同條件下互有高下。

關鍵字

階層線性模式 ； 一般線性迴歸模型 ； 組內相關係數 ； 檢定力

並列摘要

Hierarchical data contains lower level data and higher level grouping factors, which lower level data have some degree of nonindependence due to group. Hierarchical Linear Model(HLM) is a statistical method that extends traditional regression model for multilevel data.
In this paper, the comparision of HLM, and Ordinary Linear Regression(OLS) model on hierarchical data is discussed. This research conducts a simulation to contrast the probability of typeⅠerror and the power that test the fixed effect of lower level variable on HLM and OLS. The factors in the simulation are Intraclass Correlation Coefficient(ICC) and sample size.
From the simulation results show that OLS cannot control the typeⅠerror when increasing the degree of dependence on data. The power of OLS and HLM are higher than each other on different conditions, while both HLM and OLS have stable typeⅠerror.

並列關鍵字

Hierarchical Linear Model ； Ordinary Linear Regression ； Intraclass Correlation Coefficient ； Power

參考文獻

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