NLTP法非重複觀測點之缺適性檢定

NLTP Method of Lack of Fit Test for Nonrepeated observations

薄喬萍(Chiao-Pin Bao) ； 陳天惠(Tiang-Hwei Chen)

《管理科學學報》 6卷1期 (1989/05) Pp. 57-75

https://doi.org/10.6504/JOMS.1989.06.01.06

摘要

缺適性檢定是檢驗所配適的回歸模式對於元資料是否配適。傳統的迴歸分析家對於多元回歸無重覆觀測點之缺適性檢定，發展出不同的檢定方法，但”都”沒有考慮到”成本”因素。亦即檢定時間之極小化是本文研究之主要目標。首先，本文針對馬氏距離(Mahalanobis distance)公式做計算過程的簡化推演。由簡化結果可以看出，若利用Hat短陣內的元素，只須要作簡單的算術運算，而不必每求兩點距離都要經過複雜的矩陣運算了。本文並提出缺適性檢定新方法NLTP(New method of Lack of fit Test Procedure)法，此法沿襲傳統的”近鄰”(near neighbor)觀念，但避免了繁雜的矩陣運算，並透過近鄰半徑r值的變動，迴歸分析者可對檢定結果作成敏感性分析，使決策者能夠更客觀更正確地作成適當的決策。

並列摘要

Lack of fit test is the test which determine if the original data fit into the given regression model. Traditional regression analysts have developed several different methods on Lack of fit test based on multiple regression with unrepeated observed points. Those methods do not consider the “cost”factor and this is exactly the objective of this article--minimizing the time of the calculation of the test.
First, we simplify the Mahalanobis distance formula. From the derived result, we can simply apply the elements of the Hat matrix. After the simplification, only simple calculation is needed rather than a complicated matrix calculation on the distance between two points. This article also offer a new method of Lack of fit test-- NLTP. This method applys traditional concept on “near neighbor” and the complicated matrix operation is tactfully avoided. Through the variation of r -- the value of the near neighbor radous, analyst can have a sensitivity analysis on the result of the test. The decision maker can then make a more objective, correct and proper decision after the test.