Graphical Tools for the Exploration of Multivariate Categorical Data

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