臺灣博碩士論文加值系統

在現今統計建模中，有許多不同的方法可用於分析零膨脹計數數據，其中最常用的是
零膨脹模型。然而，柵欄模型的表現有較好的彈性，尤其在反應變數的零比例較低之
情況。因此，我們採用這樣的假設：反應變數的邊際分佈服從柵欄二項分配，以適應
零膨脹和零收縮的情況。此外，為了解決特定區域內重複測量所產生的時空相關性，
我們採用廣義估計方程式(GEE, Generalized Estimating Equations) 估計回歸係數。值
得注意的是，GEE 具有穩健性，即使反應變數的實際分配是未知的情況下也適用。進
一步，我們採用迭代非參數的技術更新工作相關矩陣，並使用Jackknife 摺刀法近似
GEE 之下的變異數估計，從而獲得更有效和可靠的估計。在模擬結果中，我們提出的
方法被證明有能力處理具有零調整特徵的複雜時空資料集。此外，我們也與採用不同
參數估計方法的柵欄模型進行了一系列比較分析。基於均方誤差(MSE, Mean squared
error) 測量，結果證明了相對於替代方法我們的方法更具優勢。
關鍵字：廣義估計方程式、摺刀法重抽樣、時空相關性、零膨脹、零緊縮

In contemporary statistical modeling, various techniques are available for analyzing zeroinflated
count data, among which zero-inflated models are commonly used. However,
hurdle models offer greater flexibility, especially in low-zero proportions. Thus, we adopt
the assumption that the marginal distribution of the response follows a hurdle binomial
distribution, accommodating both zero-inflated and zero-deflated situations. Additionally,
to address spatiotemporal correlations resulting from repeated measurements within
specific regions, we employ Generalized Estimating Equations (GEE) to estimate the regression
coefficients. Notably, GEE demonstrates robustness, making it suitable even
when the underlying distribution of the responses is unknown. Furthermore, we incorporate
an iteratively nonparametric technique to update the working correlation matrix
and utilize the jackknife approach to approximate the estimation variance of GEE, resulting
in more effective and reliable estimates. In the simulation results, our proposed
methodology proves to be promising for analyzing complex spatiotemporal datasets with
zero-modified characteristics. Additionally, a series of comparative analyses with alternative
hurdle models employing different parameter estimation methods are conducted.
The results demonstrate the advantage of our approach over the alternatives based on
mean squared error measurements.
Keywords : Generalized Estimating Equations, Jackknife resampling, Spatiotemporal
correlations, Zero-inflated, Zero-deflated.

摘要
Abstract
第1 章緒論
第2 章模型介紹
2.1 柵欄二項模型
2.2 柵欄二項模型之廣義估計方程式
2.3 時空相關性參數
2.4 Var(ˆβ) 之估計
第3 章模擬實驗
3.1 模擬設定
3.2 模擬流程
3.3 評估準則
3.4 模擬實驗之結果
3.5 方法比較
第4 章實際資料分析
4.1 資料說明
4.2 分析結果
第5 章結論
附錄一
附錄二
附錄三

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