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.

This study investigated bird distributions in relation to local habitat and landscape pattern and the implications which habitat fragmentation may have for woodland birds. There were two sections to the research: an experimental study investigating bird gap crossing behaviour across distances of five to 120m; and an observational study modelling woodland bird distributions in relation to local habitat and landscape scale variables in two study areas (East Loch Lomond and the Central Scotland Forest). In the experimental study it was hypothesised that bird willingness to cross gaps will decrease with increasing gap distance even at home-range scales and that the rate of decline will vary interspecifically in relation to bird morphology. Song thrush mobbing calls played at woodland edges in the West of Scotland were used to attract birds across gaps and results were compared with the response along woodland edges. Data were obtained for four species: chaffinch, coal tit, robin and goldcrest. The decline in response with distance across gaps and along woodland edge was modelled for each species using generalized linear modelling. Maximum gap crossing distances ranged from 46m (goldcrest) to 150m (extrapolated value for the chaffinch). Goldcrests responded more readily through woodlands. There was no difference between woodland edge and gap response for the coal tit. Robins and chaffinches however responded more readily across gaps than through woodland. When different response indices were plotted against bird mass and wing area, results suggested that larger birds with bigger wings responded more readily across gaps than through woodland. It is suggested that this relates to differences in bird manoeuvrability within woodlands and ability to evade a predator in gaps. Fragmentation indices were calculated for an area of the Central Scotland Forest to show how willingness to cross different gap distances influences perception of how fragmented the woodlands are in a region. Results are discussed in the context of the creation of Forest Habitat Networks. The data for the observational section of the work was from bird point counts for 200 sample points at East Loch Lomond in 1998 and 2000 and 267 sample points in the Central Scotland Forest in 1999. In addition a time series of point count data was available for 30 sample points at East Loch Lomond. Additional data was gathered for ten sample points (1998) and two sample points (2000) at East Loch Lomond to investigate effects of observer, time and weather on count data. Generalized linear and generalized additive modelling was carried out on these additional data. Results indicated that biases due to the variation in time and weather conditions between counts existed in the pure count data but that these were eliminated by reducing data to presence and absence form for analysis. Species accumulation curves indicated that two counts per sample point were insufficient to determine species richness. However a sufficiently large proportion of the species was being detected consistently in two counts of ten minutes duration for it to be valid to model them in relation to habitat and landscape variables. Point count data for East Loch Lomond in 1998 (ELL98) and the Central Scotland Forest in 1999 (CSF99) for the wren, treecreeper, garden warbler, robin, blue tit, blackbird, willow warbler, coal tit, goldcrest, great tit, and song thrush were analysed using generalized additive modelling. In addition models were built for the blackcap (CSF99) and the siskin, redstart and wood warbler (ELL98). Where all relationships were identified as linear, models were rebuilt as GLMs. Models were evaluated using the Area Under the Curve (AUC) of Receiver Operating Characteristic (ROC) plots. AUC values ranged from 0.84-0.99 for ELL98 and from 0.76-0.93 for CSF99 indicating high predictive accuracy. Habitat variables accounted for the largest proportion of explained variation in all models and could be interpreted in terms of bird nesting and feeding behaviour. However additional variation was explained by landscape scale and fragmentation related (especially edge) variables. ELL98 models were used to predict bird distributions for Loch Lomond in 2000 (ELL00) and for the CSF99. Likewise the CSF99 models were used to predict distributions for ELL98 and ELL00. Predicted distributions had useful application in many cases within the ELL site between years. Fewer cases of useful application arose for predicting distributions between sites. Results are discussed in the context of the generality of bird environment relationships and reasons for low predictive accuracy when models are applied between sites and years. Models which had useful application for ELL00 were used to predict bird distributions for 2025 and 2050 at East Loch Lomond. Habitat and landscape changes were projected based on the proposed management for the site. Since woodland regeneration rates are difficult to predict, two scenarios were modelled, one assuming a modest amount of regeneration and one assuming no regeneration. Predictions derived from the ELL98 models showed broad-leaved species increasing in distribution while coniferous species declined. This was in keeping with the expected changes in the relative extent of broad-leaved and coniferous habitat. However, predictions from the CSF99 models were often less readily explicable. The value of the modelling approach is discussed and suggestions are made for further study to improve confidence in the predictions.