Some applications of generalised linear models
This thesis is concerned with some extensions to and applications of generalised linear models and their implementation in a statistical package. The principal extension considered is the inclusion of extra parameters in the link function of the model in order to create a family of parametric link functions. This technique is applied to standard link functions as well as to the family of composite link functions. The applications of such models are illustrated by reference to several examples. The techniques presented enable complicated models to be fitted in a unified and consistent manner, without the need for specialist software or algorithms. A two-stage algorithm for fitting parametric link functions is presented and a diagnostic procedure applied to this class of extended models. The applications of such models include the analysis of grouped and multivariate data. It is shown that grouped data arising from a truncated or mixture distribution can be represented as a parametric composite link function and the technique applied to extend the analysis of some previously published data sets. Following a transformation, it is shown that certain time series models may modelled using parametric composite link functions. An algorithm is presented for the fitting of such models in which the variance function of the observations may be a quite general function of the mean. A generalisation of the multivariate logistic distribution is introduced with application to the analysis of repeated measurements data. Finally, the results of an investigation into the possible development of a statistical programming language, with particular reference to the fitting of generalised linear models, are considered. An implementation of such a language is reported and some features of the language illustrated.
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