The graphical representation of structured multivariate data

Abstract

During the past two decades or so, graphical representations have been used increasingly for the examination, summarisation and communication of statistical data. Many graphical techniques exist for exploratory data analysis (ie. for deciding which model it is appropriate to fit to the data) and a number of graphical diagnostic techniques exist for checking the appropriateness of a fitted model. However, very few techniques exist for the representation of the fitted model itself. This thesis is concerned with the development of some new and existing graphical representation techniques for the communication and interpretation of fitted statistical models. The first part of this thesis takes the form of a general overview of the use in statistics of graphical representations for exploratory data analysis and diagnostic model checking. In relation to the concern of this thesis, particular consideration is given to the few graphical techniques which already exist for the representation of fitted models. A number of novel two-dimensional approaches are then proposed which go partway towards providing a graphical representation of the main effects and interaction terms for fitted models. This leads on to a description of conditional independence graphs, and consideration of the suitability of conditional independence graphs as a technique for the representation of fitted models. independence graphs are then developed further in accordance with the research aims. Since it becomes apparent that it is not possible to use any of the approaches taken m order to develop a simple two-dimensional pen-and-paper technique for the unambiguous graphical representation of all fitted statistical models, an interactive computer package based on the conditional independence graph approach is developed for the construction, communication and interpretation of graphical representations for fitted statistical models. This package, called the Conditional Independence Graph Enhancer (CIGE), does provide unambiguous graphical representations for all fitted statistical models considered.