分段直線迴歸模式與傳統迴歸法在評估作物對環境之非線性反應的比較研究

Comparative Study of a Piecewise Linear Regression Model with the Conventional Regression Model for Assessing Nonlinear Environmental Responses of Crops

呂秀英(Hsiu-Ying Lu)

《中華農業研究》 47卷1期 (1998/03) Pp. 12-27

https://doi.org/10.29951/JARC.199803.0002

摘要

一個高適應性的作物品種，應該要對惡劣環境鈍感而對有利環境敏感，亦即這種對環境優劣表現互異的理想品種，事實上對環境呈非線性反應。傳統上常用直線迴歸分析來評價基因型的種定性，是假設基因型對所有環境具直線反應，當參試品種族群中存在有對環境優劣表現差異的基因型時，將會產生遮蓋效應而無法選出真正理想的品種，甚至將不穩定的品種誤認為是穩定。因此，本研究擬探討藉Verma and Chahal (1978)所提出之分段直線迴歸來進行穩定性分析的可行性。以玉米及水稻假設模式為基礎，各產生200套的作物區域試驗模擬資料後，再將每一套數據用傳統迴歸法及分段直線迴歸法分別進行穩定性分析，以比較這兩種方法的估計效率。結果發現，利用分段直線迴歸法較傳統迴歸法可有效地檢驗出品系對優劣環境之個別反應差異，同時用來選拔出高適應性的作物品種，可減少誤判的風險。本研究並以個人電腦之SAS軟體，編寫出一個穩定性分段直線迴歸分析程式，以本省玉米區域試驗之實例資料來說明其進行分析的流程及結果。幫助農業工作者之實際應用。最後，利用一個三度空間圖來描述各品系在優劣環境之穩定性與平均表現值間的關係，將有利於篩選出具高產且高適應性的基因型。

關鍵字

穩定性 ； 分段直線迴歸 ； 非線性反應 ； 模擬試驗 ； 假設模式 ； SAS程式

並列摘要

A high adaptable crop variety would be the one with relatively low sensitivity in the poor environments and high sensitivity in the favorable environments. That is, an ideal genotype should have nonlinear responses to environment. The conventional linear regression for stability analysis cannot detect such varieties, and an unstable variety might be wrongly regarded as stable, because the computation of the linear regression over all the environments has the masking effect on the detection of ideal genotypes, if they exist in the population. The purpose of this study was to compare the validity of the piecewise linear regression model proposed by Verma and Chahal (1978) and the conventional regression model in stability analysis. Based on hypothetical models of maize and rice, two hundred sets of simulated data generated from each hypothetical model were analyzed by each of the conventional regression and piecewise linear regression. The result showed the piecewise linear regression is useful to measure the separate responses of varieties to the defferent ranges of environments, and reduce the risk of wrongly identification. A SAS program for the piecewise linear regression analysis of stability was presented. This program runs on personal computers. The procedure was illustrated through an example of maize regional trial data in Taiwan. It is useful to agricultural researchers in application of piecewise linear regression for stability analysis. The relationship among stability in poor environments, stability in favorable environments and mean performance for each genotype was shown by a three-dimensional graph. This graph provides a direct and easy method of screening genotypes with the performance above the mean and high adaptability.

並列關鍵字

Stability ； Piecewise linear regression ； Nonlinear responses ； Simulation experiment ； Hypothetical model ； SAS program