多元t分配的效果解構

Abstract

效果解構或稱之為媒介分析在現代科學中是受到非常大注意的。其中Baron與Kenny (1986) 所提出的方法是最普遍被運用的。但這個方法其分離出來的幾種效果卻受到許多質疑。高子瑗(2015)對這些質疑提出了理論證明並且提出一種乾淨的效果解構方法，但這一切皆是在常態分配的基礎上去建立其理論的。我們這邊論文的目的在於探討當隨機變數的分配為多維度t時其 Baron 與Kenny的效果解構為何，且高子瑗的效果解構為何。在所建立的效果解構中，我們也將對未知之效果做統計推論並進行一個資料分析。其結果均詳述於文章中。

Effect decomposition or mediation analysis plays a very important role in modern research and application. The approach of Baron and Kenny (1986) is the most popular method that has been proved for its controversy by 高子瑗 (2015). 高子瑗 (2015) also provide a new method for effect decomposition with effects non-controversial. However, it is all based on that the underlying distribution of random variables involved is normal. Our purpose in this paper is to provide statistical theory of effect decompositions of Baron and Kenny and 高子瑗 all for multivariate t-distribution. Inference and data analysis are introduced.