交互作用迴歸

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。但這存在著兩個缺點：第一，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))。第二，對於傳統的觀點在交互作用的效果上，認為隨機變數X1和X2影響Y，只有反應在迴歸函數的斜率參數上，這忽略了截距參數是否也受到交互作用的影響(Baron and Kenny (1986))。 我們首先在這篇研究中提出迴歸型態的交互作用(交互作用迴歸)。並且將交互作用迴歸的參數，使用模擬研究的方式來研究其最大概似估計量(the maximum likelihood estimator)的有效性及其檢定力。

The insertion of product terms into analytical model to test for presence of interaction effect is very common in economic, social and health sciences has two disadvantages: First, it has long been criticized for that existence of interaction is model dependent (Greenland (2009) and Mauderly and Samet (2009)). Second, this classical concept for interaction effect measurement shares the unawareness in common effect identification (Baron and Kenny (1986)) measuring the influences of explanatory variables only on regression function’s slope parameters ignoring its impact on its intercept parameter. We initiate in this research in a regression set-up interaction with a systematic definition and derivation of interaction effect on the regression function. The parametric interaction regression parameters are presented and their parametric maximum likelihood estimations are introduced and verified with simulation studies. Data analysis will also be presented.