以線型混合模式與廣義估計方程式分析生物防治資料

Abstract

縱向資料(longitudinal data)為同一個體,在不同時間下,經重複觀測而得的資料。因由同一個體而來,所以其觀測值就不獨立,例如:藥物試驗時,每個病人在每個時間點觀測藥效變化,則同一個病人測的資料,有相關性存在;又如農業方面,尤其是多年生作物,測其肥料、農藥......等影響,也常用重複觀測得到資料。因為這種資料具有相關性存在,所以無法使用一般的迴歸分析或變方分析,必須使用其他一些特別模式分析,常用的方法有線性混合模式(linear mixed model)和廣義估計方程式(generalized estimating equation)來分析。 廣義估計方程式為將相關的資料以群聚(cluster)的方式組合,並且把整組資料視為彼此獨立的群聚,再以群聚為單位用一般線性迴歸分析。線性混合模式比一般線性模式使用更廣泛,此因它可以同時估計固定效應和隨機效應,使得一些有相關性的資料,變成可以分析。 本篇文章將利用一筆由國立屏東科技大學植物保護系 生物防治研究室提供,將木黴菌拮抗立枯絲核菌的功效,經過一段時間重複觀測所得的資料。詹(2003)曾用生物檢定法(biological assay)做過分析。本文我們將八種木黴菌重複測量的觀測值,視為隨機效應;木黴菌品種視為固定效應,用線性混合模式和廣義估計方程式進行分析,並比較各木黴菌品種抗立枯絲核菌的效能,再將結果和詹(2003)結果比較,判別方法的優劣。

Longitudinal data can be obtained by observing same object at different time. So the observations are not indepedent with each other.In drug experiment,observations on the reactions of the same patient at different time are not mutually independent. In agriculture,the effect of fertilizers or insecticides can be treated as longitudinal data too, especially for perennial crops. Because of the existence of correlations between observations,it is not appropriate to use general regression analysis or ANOVA.Linear mixed model and generalized estimating equation are two kinds of methods often used in analyzing longitudinal data.

Generalized estimating equation divides data into different clusters by their correlations.Then it can be analyzed by general regression analysis ,assuming that the clusters are independent with one another.Linear mixed model is used more often,because the model can be used to analyze the data with fixed and random effect at the same time. The data used in the thesis was provided by Biological Control Laboratory in Department of Plant Protection in National PingTung University of Science & Technology.The main interest is to know the effect of Trichoderma spp. on Rhizoctonia solani with repeated measure data. Chan(2003) analyzed the data by using the method of Biological assay.This thesis analyzes the same data by using linear mixed model and generalized estimating equation.The effect of seven species of Trichoderma spp. is fixed effect and the effect of observations from repeat measurement is random effect.The results are also compared with those obtained by Chan(2003).