脊估計法在徑路分析上之應用

A Study on Ridge Estimation of Path Analysis

常用之徑路係數不偏估計式：（公式請見內文）在統計理論上雖具備諸多優良性質：如不偏性、有效性、不變性、充份性等，然在均方誤差（MSE）風險準則下，卻並非 最佳估計式，尤其當自變數間呈現高度共線性（multicallinearity）情況時，所估得之徑路係數之大小及正負符號常不盡合理，致使因果關係之解釋與實際現象大有出入。本文建議利用具有較高精密度之脊估計法，進行估計，可求得改進之徑路係數（公式請見內文），至於脊做式中最佳脊係數K值之求取，至今未得定論，本文建議採用在徑路係數機差均方（mean square error of path coefficients）為最小之原則下所求得之k值為最適值，本文除原理之簡介外，特別提出「八十一學年度某師院初等教育學系畢業生報考本院初等教育研究所之教育研究法成績與其大學相關科目成績之路徑分析的應用實例」，以利讀者參閱。

The purpose of this study is to give an improved solution in path analysis. It is found that the path coefficients， estimated in form of （公式請見內文） by least square method are poor if the independent variable are in multicollinear condition. However， the path coefficients are improved through the biased estimation in the form of （公式請見內文）. It is bright to compare the difference with suing the given educational datum. As for the ridge coefficient K value in biased estimation， it is obtained under the minimum square error of path coefficients.