My Masters research aims to deepen our understanding of the behaviour of robust methods in logistic regression. Logistic regression is a special case of Generalized Linear Modelling (GLM),which is a powerful and popular technique for modelling a large variety of data. Robust methods are useful in reducing the effect of outlying values in the response variable on parameter estimates. A literature survey shows that we are still at the beginning of being able to detect extreme observations in logistic regression analyses, to apply robust methods in logistic regression and to present informatively the results of logistic regression analyses. In Chapter 1 I have made a basic introduction to logistic regression, with an example, and to robust methods in general. In Chapters 2 through 4 of the thesis I have described traditional methods and some relatively new methods for presenting results of logistic regression using powerful visualization techniques as well as the concepts of outliers in binomial data. I have used different published data sets for illustration, such as the Prostate Cancer data set, the Damaged Carrots data set and the Recumbent Cow data set. In Chapter 4 I summarize and report on the modem concepts of graphical methods, such as central dimension reduction, and the use of graphics as pioneered by Cook and Weisberg (1999). In Section 4.6 I have then extended the work of Cook and Weisberg to robust logistic regression. In Chapter 5 I have described simulation studies to investigate the effects of outlying observations on logistic regression (robust and non-robust). In Section 5.2 I have come to the conclusion that, in the case of classical or robust multiple logistic regression with no outliers, robust methods do not necessarily provide more reasonable estimates of the parameters for the data that contain no strong outliers. In Section 5.4 I have looked into the cases where outliers are present and have come to the conclusion that either the breakdown method or a sensitivity analysis provides reasonable parameter estimates in that situation. Finally, I have identified areas for further study.
|Date of Award||2005|
|Supervisor||Shuangzhe Liu (Supervisor) & Alice Richardson (Supervisor)|