三因子之調節複迴歸：斜率差異檢定法的應用

Abstract

迴歸分析已經是個相對成熟的資料分析工具，不管是管理、心理、生物、經濟等各大領域的研究者、資料分析使用者甚至是決策者無不利用迴歸模型的建立來萃取隱藏在數據裡的重要資訊，因此如何建立適當的模型來了解變數間關係的議題一直是統計學家所關心的。本文專注於了解一般研究者容易忽略的三因子交互作用的迴歸模型，提出對於該模型在資料分析的過程中應該注意的事項以及分析流程的建議，並且推薦利用斜率差異檢定法做為工具來了解:具有三因子交互作用時應該如何做往後的分析，同時也因為斜率差異檢定法的重要性，本文透過蒙地卡羅模擬法來了解其檢定力與自變數相關係數兩者之間的重要關係，此為相關文獻中尚未清楚說明的部分，也為本研究的主要貢獻。

Regression analysis is a very popular tool for data analysis in many areas, such as man-agement, psychological, biological, economic, and so on. Researchers and decision-makers usually extract important information from the data by using this tool. But how to build an adequate model to understand the relationship between variables is a big problem. This article focus on three-way interactions model of regression analysis (or moderated multiple regres-sion ) which sometimes has been overlooked. In fact, slope difference test is the best approach when three-way interactions has been detect. For this reason, this article present a recom-mended process about three-way interactions model, something must be pay attention and show the relationship between power and intercorrelation between predictor variables about slope difference test by Monte Carlo simulation.