Three-way methods for the analysis of qualitative and quantitative two-way data.

A problem often occurring in exploratory data analysis is how to summarize large numbers of variables in terms of a smaller number of dimensions. When the variables are quantitative, one may resort to Principal Components Analysis (PCA). When qualitative (categorical) variables are involved, one may choose from a variety of methods which are adaptations of PCA, designed for this purpose. This book is about such adapted PCA methods for qualitative variables, and for mixtures of qualitative and quantitative variables. Part I treats adapted PCA methods, like Multiple Correspondence Analysis (MCA), in retrospect. The methods are systematized such that the choice between the different methods is facilitated. In order to fill certain gaps in this system a number of new methods is developed. One of these new methods is discussed in detail in Part II, which contains various innovatory contributions. One of the main new developments is the construction of techniques for rotating the MCA solution to what is called simple structure. These techniques are generalizations of the well-known VARIMAX and QUARTIMAX techniques for rotating PCA solutions. The former rotation techniques are implicitly constrained in the sense that the new components are rotations of the MCA solution. In order to optimize VARIMAX or QUARTIMAX from the start a different technique is offered in which this constraint is dropped. This new technique, which is based on INDSCAL, finds solutions in which clusters of variables are identified more clearly than is done in MCA, even after simple structure rotation. An important additional consequence of this is that the observation units (objects, individuals) are also represented more clearly in clusters than is the case with MCA, which implies that the method is useful as a cluster technique. Finally, Part III shows how certain selected methods work in practice. For this purpose seven example data sets have been analyzed. The results are discussed in detail, including some stability analyses. Particular attention is paid to the clustering of variables and objects.