Multinomial Repeated Measurements Analysis in Baseline-Categorical Logit Model

• Main Authors: Ya-Chin Yeh, 葉亞青
• Other Authors: Chien-Hua Wu
• Format: Others
• Language: zh-TW
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/34840324248603540597

碩士 === 中原大學 === 應用數學研究所 === 97 === 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.