針對百分比資料，我們通常假設資料是符合貝他分配(beta distribution)，以進行分析。然而，在實際應用中，往往無法確定資料的真實分配，這可能會導致對感興趣參數的統計推論出現錯誤。 本文運用強韌化負二項實作概似函數，分析百分比資料。 透過模擬和實例分析，我們呈現了強韌華德檢定統計量(robust wald statistics)、強韌分數檢定統計量(robust score statistics)、強韌概似比檢定統計量(robust likelihood ratio statistics)，以及各個檢定的信賴區間(confidence interval)與覆蓋機率(coverage probability)。 我們比較此方法與貝他迴歸模型在分析百分比資料時的差異與優缺點。通過 簡單迴歸說明，當資料為獨立且同分配(independent and identically distributed, iid)時，隨著樣本數增加，能看出貝他迴歸模型在檢定時會產生錯誤。而在非 iid 的迴歸架構下，貝他迴歸模型的參數估計量已會有明顯的錯誤。使用本文提出的方法，即使未知資料的真實分配，我們仍能得到正確的統計推論，且更適用於實際情況。 ;Percentage data can be analyzed based on beta distribution. However, in practical applications, we often cannot determine the true distribution of the data, which could result in incorrect statistical conclusions regarding the parameters of interest. This thesis proposes a robust likelihood function method to analyze percentage data. It presents robust Wald statistics and robust score statistics through simulation and case analysis. We compare the differences, advantages, and disadvantages between this method and the beta model in analyzing percentage data. Using simple regression as an example, when the data are independently and identically distributed (iid), as the sample size increases, it becomes evident that the beta model produces errors during hypothesis testing. In situations where the data are not iid, the parameter estimates from the beta model exhibit significant errors. Our proposed method can make correct statistical inferences even though using a misspecified model.
