廣義估計方程式與廣義線型混合模式在入侵紅火蟻試驗資料的應用

Abstract

2003年10月行政院農業委員會動植物防疫檢疫局證實在台灣發現入侵紅火蟻，地點主要是台北縣、桃園縣及嘉義縣等地。為了降低入侵紅火蟻在台灣所造成的損失及其族群數量，植物防疫檢疫局核准了芬普尼、百利普芬及賜諾殺這三種入侵紅火蟻的防治用藥，以供大眾使用。為了解藥劑的防治藥效，行政院農業委員會所屬的桃園農業改良場研究員施錫彬，及台南農業改良場研究員陳昇章、林明瑩、黃淑惠等人進行了相關的試驗。試驗地點分別在桃園縣八德市及嘉義縣水上鄉。本文目的即根據試驗結果配適模式並估計藥劑的防治率。 因為試驗資料類型為縱向資料，觀測值間有群內相關的存在， 不適合直接利用一般前提假設為觀測值間為獨立的廣義線型模式配適，所以利用廣義估計方程式與廣義線型混合模式對入侵紅火蟻防治用藥的試驗結果進行模式的配適，配適的結果顯示，利用廣義估計方程式與廣義線型混合模式所得到的平均值模式的結果是非常一致的。且三種藥劑對於入侵紅火蟻均有顯著的防治效果，在施藥後第八週時，防治率可達50 % 以上。在不同地區施用藥劑的結果經檢定後可得，蟻塚數下降的趨勢為一致，所以藥劑的藥效不會因在不同地區而有所不同。

The aim of this study is to estimate the control rate of three bait-formulated insecticides of red imported fire ants. Two field experiments were conducted, respectively, in Taoyuan and Chiayi county where the red ant infestation were spotted and the three different insecticides applied are Fipronil, Pyripronxyfen and Spinosyns. Repeated counts of ant mound number in each field plot of size 100 $m^2$ were recorded by the researchers in the local agricultural experimental station during the period of eight weeks. Two statistical procedures were employed to analyzed these two data sets and both are of generalized linear models. First one is a GEE model and the second one is a generalized mixed-effects model (GLMM). The former is relatively easy however the later demands more effort to determinea decent model. The estimates of control rate resulted from GEE and GLMM are quite similar though the standard errors are different substantially. We recommend that the SE's due to GLMM be applied to construct relevant confidence intervals, since variance structure of GLMM does have a better description to the variation of data collected. One interesting result is that all three insecticides show remarkable consistancy in control rates in the two experiment sites.