交互作用迴歸與效果迴歸之關係

Abstract

分析迴歸模型時運用插入一個相乘項到模型中，來判斷是否兩個解釋變數間存在交互作用的方式是非常普遍用於經濟、社會、和生物科技的研究。但學者長期爭議模型中交互作用項的型態。為什麼是某一種相乘項而不是另外一種相乘項。對於不同的資料，可能是用不同的型態來呈現交互作用項（Greenland (2009) and Mauderly）and Samet (2009))。這篇文章的主要目的在於把效果解構(Effect decoposition)的觀念與交互作用的觀念做一個聯結，讓我們更清楚瞭解交互作用該如何分析。另外我們也提出一個概念，也就是一個新的交互作用分析也可以應用在分位迴歸的問題上。我們在分位迴歸的交互作用分析上做了一個均方誤差的模擬分析。

The aim of this paper is to make a connection between interaction and effect decomposition. We show that the approach of inserting a product term in regression model for assessment of interaction is completely affected by effect decomposition. That is, when a regression model is linear in x_1 and x_2, then the coefficients of these two variables are treated as dived effects of x_1 and x_2, effect not mediated by other variables. Hence a linear function cannot produce interaction effect and then it is forced to add a product term as possible interaction variable. We have a detailed description of these two approaches and extend the interaction study to the quantile regression model.