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 st~ong 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.
| Identifer | oai:union.ndltd.org:ADTP/218743 |
| Date | January 2005 |
| Creators | Nargis, Suraiya, n/a |
| Publisher | University of Canberra. Information Sciences & Engineering |
| Source Sets | Australiasian Digital Theses Program |
| Language | English |
| Detected Language | English |
| Rights | ), Copyright Suraiya Nargis |
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