Graphical Tools for the Exploration of Multivariate Categorical Data

Categorical data appear in all areas of data analysis from social sciences and surveys to data mining. They occur either in the form of nominal or ordered variables and interval grouped data as in (possibly censored) data of statistical offices. As computers and methods are able to handle ever larger data sets the importance of analysing categorical data grows accordingly. Approaches are made in this direction but often enough the analysis remains on the level of merely a listing of numbers. Data mining plays an especially large role since in this field categorical data are not only analysed but also vast amounts of categorical output are produced and have again to be analysed in order to obtain interpretable results. In the field of statistical modelling there are several approaches in dealing with multivariate categorical data - linear and log-linear models logit and probit models are some of the most common methods. For all of these methods it is necessary to check how well the data are fitted. Examining residuals with respect to structural behaviour or irregularities is vital. In the case of continuous data graphical displays are used for this task. For categorical data graphical displays also exist even for high-dimensional situations. But the connection between the graphical display and the model is far less explored for categorical data than for continuous data.