兩種生物多樣性指標估計模擬研究-比較偏性矯正與信賴區間涵蓋率

A Simulation Study of Two Biodiversity Index Estimation Procedures-In Comparing Bias Correction and Confidence Interval Coverage Rate

楊滿霞(Man-Hsia Yang)

指導教授 ： 彭雲明

國立臺灣大學/生物資源暨農學院/農藝學研究所/碩士(2006年)

https://doi.org/10.6342/NTU.2006.02640

摘要

Shannon指標是最廣為使用的物種多樣性指標,
傳統的Shannon指標測量為MLE估計法,
但是沒有取樣到的物種數增加時, MLE估計值有明顯低估的情形。
Chao和Pla這兩位教授在差不多時間(Chao, 2001年12月和Pla,2001年5月),
提出矯正Shannon指標低估的方法,
Chao利用Horvitz-Thompson估計量來矯正沒有被取樣到的物種，
與sample coverage的觀念給予物種相對豐量適當的估計，結合這兩種理論方法來矯正Shannon指標;
Pla使用拔靴估計值和樣本估計值的偏差對樣本估計值和
群落Shannon指標的偏差來建立經驗矯正式,獲得矯正估計值與信賴區間,可以看出兩人所使用的估計方法大為不同。

本篇論文比較了兩種估計方法的矯正偏性的能力與信賴區間涵蓋率，
經電腦模擬顯示,在大部分的情形下,兩種矯正估計值幾乎沒有偏性的情形,
只在取樣數少且群落相對豐量歧異度大時,兩種矯正估計法仍獲得低估的估計值,
但是低估的程度不若MLE估計法嚴重。
最後在四個實例的估計結果中發現， Chao和Pla兩種矯正估計值皆較MLE估計值高,
說明兩種估計矯正值確實矯正MLE估計法低估的情形。

Pla使用矯正的估計值和拔靴標準誤差來建立矯正的信賴區間,
矯正後的信賴區間涵蓋率明顯高於標準百分比法和矯正百分比法,
但是仍然未達到名義上涵蓋率的要求，在電腦模擬的資料中發現，
拔靴標準誤差小於模擬後所得估計值的標準誤差。
使用calibrating回歸式矯正拔靴標準誤差偏小的情形,
四個模式和委內瑞拉的模擬結果, calibrating變方矯正值使得信賴區間涵蓋率提升到90%以上,
說明calibrating變方矯正值使得涵蓋率名實相符。

關鍵字

生物多樣性指標 ； Shannon指標

並列摘要

The most widely used measure of species diversity is Shannon index.
The traditional MLE method provides a biased estimator. The ML estimator tends to be underestimated,
especially when the number of unsampled specises increasing.
Chao and Pla proposed estimation methods that would adjust underestimated problems at almost the same time (Chao, December 2001, and Pla, May 2001).
Chao's estimation procedure combines the Horvise-Thompson(1952) adjustment for missing species and
the concept of sample coverage,
which is used to properly estimate the relative abundance of species discovered in the sample.
Pla proposed a technique using the difference of the original sample and
each bootstrap replication to constract an empirical adjustment for the bias,
and result in an adjusted point estimator and corresponding confidence interval.
Clearly, they used very different estimation procedures to estimate Shannon index.

In this study, we are interested in comparing the two estimation procedures in bias correction and
confidence interval coverage rate.
According to computer simulation results,
the two estimation procedures works well in adjusting underestimated in most conditions.
Only in small sample size and large diversity of relative abundance scenero,
the two estimation procedures are still underestimated, but less serious than MLE method.
Finally, we use four real examples to illustrate that
the two estimation procedures reveal the ability of adjusting underestimations.
They both have higher estimations than the traditional MLE method.

Pla used adjusted point estimation and the bootstrap standard deviation to estimat the adjusted confidence intervals.
The adjusted confidence interval coverage rate is highter than the standard percentile method and
corrected percentile technique, but still not provide the nominal coverage rate.
By computer simulation results, I discover that bootstrap variance is smaller than simulation variance.
Applying calbrating regression technique to adjust bootstrap variance allows us to recover the nominal coverage rate.
In four models and Venezuela simulations,
the adjusted variance by calibrating raises to a 90\% coverage.
Using adjusted variance to construct adjusted confidence intervals really can reach nomial coverage rate.

並列關鍵字

biodiversity ； Shannon index

參考文獻

處與國立台灣師範大學生物學系合作研究, http://www.kmnp.gov.tw/chinese

Chao A. and Lee S.M. (1992), "Estimating the Number of Classes via Sample Coverage,"

Journal of the American Statistical Association, 87, 210-217.

Chao A. and Shen T.J. (2003), "Nonparametric estimation of Shannon's index

Gaston K.J. (1996), Biodiversity : A Biology of Numbers and Difference: Blackwell Science.