再探討參考曲線相等性之假設檢定

Abstract

探討兩個團體之個體之成長曲線是否相同在文獻上已有些許討論。但，這些討論大都侷限在代表兩個成長模型之迴歸線參數是否相等的問題上打轉。近來，張（2010）提出詳細之迴歸參數關係用以表現兩個成長曲線相等的問題。這個關係清楚說明如何借由參數之檢定達到是否兩團體參數曲線相等之探討。張（2010）也介紹了最大概似比之檢定。這個方法為有母數且較繁複。我們介紹廣義最小平方法之檢定並做了許多模擬分析。

關鍵字：假設檢定；線性迴歸；檢定力；參考曲線；參考區間；迴歸分位數

Comparisons of reference charts for verifying if two populations of subjects have the same growth pattern have received some attention in literature. However, the proposals of comparison are restricted on equalities of regression parameters or regression functions. Recently, Zhang ( 2010 ) has a detailed description for relationships between model parameters and equalities of reference charts that provides a precise indication for verifying if reference charts in two models are identical. She also proposed the likelihood ratio technique as a test for this verification. We re-visit this problem with the generalized least squares estimation and use it to construct the classical F test. Through simulation study, we see that this proposal is very competitive in reference charts comparison.

Key words: Hypothesis testing; linear regression; power; reference chart;reference interval; regression quantile