The Analysis of Repeated Measurement for Categorical Response Data by Using Conditional Distribution Model

• Main Authors: Lee, Tzzy-Chi, 李子奇
• Other Authors: Pong Yun-Ming
• Format: Others
• Language: zh-TW
• Published: 1997
• Online Access: http://ndltd.ncl.edu.tw/handle/49933711763375912383

碩士 === 國立臺灣大學 === 農藝學系 === 85 === This thesis focuses on the analysis of repeated measurement data of two occasions only. In some biomedical research, the first measurement is referred as initial distribution and the interests of investigation is the distribution of the second measurement. This thesis will discuss only thiskind of data. For the contingency tables resulted from repeated measured data, the statistical analysis usually try to model the marginal distributions of the first measurement and second measurement. If the goodness of fit is good enough then the model can be used to describe the data and comparisonscan be made between treatment groups or between occasions. Usually the similarity of the initial distributions of several treatment groups can bemade possible by good randomization scheme. One question is raised by the author: When the initial distributions of several treatment groups are quite different, will the statistical analysis end by wrong conclusions? The author assumes the treatment effects are all equivalent and use various hypothetical data sets with different initial distributions to study the raises dquestion. The result shows that the ordinary analysis of marginal distributions is quite robust in the sense of type I error. Only inthe data sets with extremely different initial distributions, wrong conclusion is reached, that is, treatment effects are declared statistically significant. An unusual way of analyzing this kind of data which was proposed by Agresti (1990) is also investigated by the author. Instead of modeling the marginal distributions, Agresti suggested an alternative by modeling the conditional distributions. Namely, the conditional distributions of the second occasion given thedistribution of thefirst occasion. This kind ofanalysis is free of the influence ofinitial distributions. Contrast to this,marginal distributions inthe second occasion are averages of conditional distributions weighted by the initial distributions. This thesis reveals that detailed analysis can be made by this kind of analysis which can notbe reachedby the analysis of marginal distributions. Thus, the conclusion of this thesis is: An analysis of marginal distributions may be run as a preliminary analysis, since it is quite robust forthe situation of different initial distributions. Then for obtaining amore detailed analysis, we can run an analysis by modeling the conditional distributions.