廣義Neyman-Rubin的因果模型在評估迴歸上交互作用的應用

Abstract

儘管在經濟，社會和健康科學上，藉由插入一個分析模型的相乘項來檢定交互作用影響的表現是非常常見的，但交互作用是否存在決定於模型型態為一直被批評的地方(Greenland (2009) and Mauderly and Samet (2009))。有些文章努力解決這個爭議性問題但卻導致於更複雜且不清楚的交互作用定義。這讓評估統計交互作用更加困難(Greenland (1980))。我們提出一個有系統的定義介紹，方法和定理將相互關係(結合)參數融入在廣義Neyman-Rubin的因果模型。這項創舉帶來許多的優點： (a) 此方法允許我們定義和測量關於未知統計上交互作用的統計推論的相互關係影響。 (b) 對於統計上交互作用的統計推論全都可從分佈參數的估計理論來建構。 (c) 此因果模型測量一個明確且模型獨立能避免插入爭論的相互關係影響。 (d) 廣義Neyman-Rubin的因果分析理論擴展到對於probit迴歸的統計交互作用評估。

Although the insertion of product terms into analytical to test for presence of interaction effect is very common in economic, social and health sciences, it has long been criticized for that existence of interaction is model dependent (Greenland (2009) and Mauderly and Samet (2009)). The efforts for resolving this criticism leads to multiple but ambiguous definitions of statistical interaction resulting in assessing various but unknown versions of effect (Greenland (2009)). We report that a systematic introduction of definitions, methods and theorems to fit the intercorrelation (association) parameter into a generalized Neyman-Rubin’s causal model brings interesting advantages: (a) This approach allows us to define and measure a clean effect of intercorrelation for statistical inferences of unknown statistical interaction. (b) Statistical inferences for statistical interaction all can be constructed from the estimation theory of the distributional parameters. (c) This causal model measures an unambiguous but also model independent effect of intercorrelation that avoids the controversy of insertion. (d) The theory of the generalized Neyman-Rubin’s causality is extended to statistical interaction assessment for probit regression.