以廣義估計方程式分析影響陽明山地區之降雨量因素

Using Generalized Estimating Equations Analysis Rainfall in Yangmingshan National Park

戴宇宏(Dai Yu-Hong)

指導教授 ： 程毅豪 ； 呂翠珊

國立臺灣師範大學/理學院/數學系/碩士(2021年)

https://doi.org/10.6345/NTNU202100473

摘要

當個體只有一個觀測值，廣義線性模型(McCullagh & Nelder, 1983)已經被廣泛的用來求得參數估計；當個體不只一個觀測值，觀測值趨近於常態分配，這種統計模型已經提出(Laird & Ware, 1982)；當我們是離散型觀測值，統計方法也被多人提出(Ochi & Prentice, 1984. Laird & Ware, 1984. Koch, 1977)；當個體不只一個觀測值，並且觀測值非常態時，這種統計方法是廣義估計方程式(Liang & Scott L, 1986)。此篇論文分析竹子湖觀測站的氣象觀測資料，從廣義線性模型進一步延伸，利用廣義估計方程式分析長期追蹤資料，再利用廣義估計方程式中模型選擇的方法QIC，選取適合的模型，以實際例子進行操作說明。

關鍵字

廣義線性模型 ； 廣義估計方程式 ； QIC

並列摘要

If each subject has only one observation, then the generalized linear model (McCullagh & Nelder, 1983) had been used to obtain parameter estimate. If each subject has more than one observation and observations tend to follow normal distribution, this statistical model has been proposed (Laird & Ware, 1982). If we have discrete observations, then this statistical model also has been proposed (Ochi & Prentice, 1984. Laird & Ware, 1984. Koch, 1977.). If there is more than one observation and observations do not tend to follow normal distribution, this statistical model is Generalized Estimating Equations(Liang & Scott L, 1986). This thesis analyzes the meteorological observation data of Zhuzihu and we use the generalized estimation equation to analyze the longitudinal data. And then we use the method of model selection of generalized estimation equation, QIC, to choose the best model. We take an example by using this method of model selection.

並列關鍵字

generalized linear model ； generalized estimation equation ； QIC

參考文獻

James Cui (2007). QIC program and model selection in GEE analyses. The Stata Journal 7, Number 2. 209-220.

Liang, Kung-Yee & Scott L. Zeger (1986). Longitudinal data analysis using generalized linear models. Biometrika 73, 1. 13-22.

Mehdi Bahrami & Mohammad Reza Mahmoudi (2020). Rainfall modelling using backward generalized estimating equation: a case study for Fasa Plain, Iran. Meteorology and Atmospheric Physics 132:771-779.

Wei Pan（2001）. Akaike's Information Criterion in Generalized Estimating Equations. Biometrics, Vol. 57, No. 1. (Mar., 2001): 120-125.