交互作用迴歸的進一步分析

Abstract

檢驗一個迴歸模型是否存在交互作用在經濟、社會以及健康科學等領域有重要的應用。通常其方法是加入相乘項，再由資料檢定相乘項係數是否為零來判定是否有交互作用。但這方法的檢定力通常很低，而且其檢定結果決定於所採用的模型。溫俞婷(2015)提出一個沒有爭議的建構交互作用迴歸的方法。我們改進溫的方法把交互作用迴歸寫成迴歸係數的函數，使我們可以用最小平方法的理論來進行對交互作用的統計推論。我們也推廣交互作用到有多個解釋變數的理論。同時也進行了統計推論以及資料分析，其結果均詳述於本論文中。

Detection for presence of interaction effect by insertion of product term in a regression model is very common in economic, social and health sciences. This is criticized for model dependence and lower power in testing hypothesis .Yu-Ting Wen (2015) presents a general method to develop a clean interaction regression function that improves the power for detection and is not model dependent. Instead of presenting the interaction as a function of distributional parameters, we formulate the interaction in terms of regression coefficients allowing statistical inferences of interaction by the theory of least squares method. We also extend the interaction for the multiple explanatory variables. Inferences and data analysis are performed and results are presented.