- 學位論文
以基線類組邏輯斯模型分析多項式重複測量
Multinomial Repeated Measurements Analysis in Baseline-Categorical Logit Model
摘要
本研究主要分為六大部分，第一部分為說明研究背景、研究目的；第二部分為文獻探討；第三部份為研究方法，說明本研究的理論推導及所使用的模型；第四部分為模擬分析，運用新、舊模型於模擬數據中，觀察其分析結果；第五部份為實例分析，將上述新、舊模型運用於實例中，觀察其分析結果；最後一部份為本研究之結論，將利用第四章與第五章所得結果，來說明新、舊方法的差異性以及其優缺點。 主要的數學理論有多項式分配（Multinomial Distribution）、加權最小平方法（Weighted Least Squares，簡稱為 WLS）、類別型資料（Categorical Data）、基線類組邏輯斯模型（Baseline-Categorical Logit Model）、Wald test。 在重複測量試驗中，以往常用單純的廣義線性模型（General Linear Model，簡稱為GLM）進行資料分析，當應變數屬於類別型資料時，廣義線性模型直接將資料先行分組，分別計算出估計值之後進行資料分析，本研究將利用基線類組邏輯斯模型對資料進行分析，最後針對兩種模型所得到的分析結果進行比較，比較兩種模型的準確度以及優缺點即是本研究的目的。 在數據分析的部份，本文針對新、舊方法估計值與本文所設之母體機率計算偏差（Bias）以及均方誤差（MSE），結果顯示出利用基線類組邏輯斯模型所計算出的均方誤差皆小於或等於利用廣義線性模型所得均方誤差，進而分別對其結果進行假設檢定，檢定結果顯示兩種方法所得之拒絕率相同。總和以上結果，可得知基線類組邏輯斯模型所估算出的樣本機率較為接近實際的母體機率，而在檢定方面，其效果與廣義線性模型相同。
並列摘要
This research mainly divides into six major parts, the first part explains the research background and the research goal; the second part is the literature discussion; the third part is the research technique, which explains the theory inferential and the used model; the fourth part is the simulation analysis, utilizes above, the old model and the new model to analysis analog data, observation analysis result; the fifth part is the example analysis, above new model and old model analysis example, observation analysis result; last part is this research conclusion, uses fourth chapter and the fifth chapter of result, explains the difference between the new model and the old model. The main mathematics theory contains Multinomial Distribution, Weighted Least Squares, Categorical Data, Baseline-Categorical and Wald test. In the repeated measure experiment, commonly used General Linear Model to carry on the data analysis when the variable belongs to the categorical data, General Linear Model groups the data, calculates the estimated value then to carry on the data analysis, this research using Baseline-Categorical Logit Model to estimate the data then carries on the data analysis. Finally aims at the analysis which two kinds of models obtain to estimate and analyzes the result to carry on the comparison, compared with two kind of model's accuracies are this research goals. In the data analysis part of this paper, this article uses the estimated value is obtained from the new method and the old method, and the hypothesis parent substance probability to calculates Bias and MSE, the result showed calculates MSE from Baseline-Categorical Logit Model is smaller than or was equal to that obtains MSE from General Linear Model, then carries on the hypothesis testing to the results separately, the testing result showed that two methods obtained reject rate to be the same. Because of the above result, may know the sample probability which Baseline-Categorical Logit Model estimates to be quite close the actual parent population probability, but in the testing aspect, the effect is the same.
參考文獻
延伸閱讀
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