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研究生:廖大經
研究生(外文):Liaw, Dah-Jing
論文名稱:Richards函數之求配方法的比較研究
論文名稱(外文):Comparative Study on the Fitting Procedures of Richards Function
指導教授:林俊隆林俊隆引用關係---
指導教授(外文):Lin Jiunn-Lung
學位類別:碩士
校院名稱:國立中興大學
系所名稱:農藝學研究所
學門:教育學門
學類:專業科目教育學類
論文種類:學術論文
論文出版年:1996
畢業學年度:84
語文別:中文
論文頁數:80
中文關鍵詞:非線性回歸分析
外文關鍵詞:Richards 函數Richards functionnonlinear regression
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就Richards 函數的求配而言,若以 Causton(1969)與林(1983)所
提出的起始值搜尋法以及本研究將 Causton 法略作修飾而得的起始值搜
尋法(以下簡稱 C1、L 及 C2 法),配合 SAS/STAT 之 PROC NLIN 中所
提供的 DUD、Gauss、Gradient、Marquardt 以及 Newton 之 5 種迭代演算
法,則共可組合成 15 種不同的求配程序。本研究之目的即在循模擬試
驗的途徑,評估這 15 種求配程序的效率。

先由文獻中蒐得參數估值差異甚大的 8 個由實測數據求配而得的
Richards 函數,做為假設模式。再以這 8 個假設模式為基礎,個別以模
擬取樣法產生 500 或 1000 套變方均質的生長數據。而後再以每一套數據
用前述 15 種程序分別進行 Richards 函數的求配;並根據這些求配的結
果來探討由各種求配程序所得之參數估值的取樣分布。

就起始估值之搜尋法而言,L 法的表現很明顯地比其他兩個方法
差;而 C2 法雖略優於 C1 法,但兩個方法的表現並無很大的差異。而就
迭代演算法的比較而言,概以 Gradient 法或 Newton 法的估算結果最不
可靠;Gauss 法與 Marquardt 法的表現幾乎完全相同;而 DUD 法的表現
最優。整體而言,在本試驗的範圍內,對 Richards 函數的求配,並無一
種求配程序具有 UMVUE 的性質。但除了對一個生長型式趨近於
Gompertz 模式的假設模式之外,概以 C1+DUD 或 C2+DUD 兩個求配程
序所得的估值之取樣分布最接近 UMVUE 的性質。
When fitting growth data to Richards function, three methods of
finding initial estimates for parameters are available, namely, the
methods given by Causton (1969) and Lin (1983), and a method modified
from Causton''''s method (denoted respectively as C1, L, and C2). Hence
there is a wide choice of estimation procedures if we combine these
three methods with the five iterative algorithms provided by the PROC
NLIN in SAS/STAT, namely, DUD, Gauss, gradient, Marquardt, and Newton.
The purpose of this simulation study was to assess the validity of these
15 fitting procedures of Richards function.

Eight fitted Richards functions, differed widely in their parameter
estimates, were collected from literature to work as hypothetical models.
Five hundred or 1,000 sets of homoscedastic data generated from each
hypothetical model were then fitted to Richards function by each of the
15 estimation procedures. Thus the sampling distribution of the parameter
estimates obtained by each procedure could be investigated and compared.

The result showed clearly that L method was the least satisfactory
among the three methods of finding initial estimates. Although C2
occasionally did better than C1, no substantial difference in performance
was detected between the two methods. The final parameter estimates
obtained by gradient or Newton algorithms were generally less satisfactory
than those obtained by the other three algorithms. Gauss and Marquardt
algorithms worked quite well and gave virtually the same results. For
most of the hypothetical models, the final parameter estimates obtained by
DUD seemed the most reliable among the five iterative algorithms. In sum,
over the range of this simulation experiment, we found no one of the 15
procedures could be ranked as the UMVUE. However, the sampling
distribution of the estimates obtained by the procedure made up of C1 (or
C2) and DUD seemed to possess most of the characteristics of a UMVUE,
if one hypothetical model with nearly the Gompertz growth pattern was
deleted from consideration.
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