ABSTRACT
As was shown in Chapters 7 and 8, there are several alternative definitions of CA and different ways of thinking about the method. In this book we have stressed Benze´cri’s geometric approach leading to data visualization. In Chapters 18 and 19 it was clear that the passage from simple two-variable CA to the multivariate form of the analysis is not straightforward, especially if one tries to generalize the geometric interpretation. An alternative approach to the multivariate case, which relies on exactly the same mathematics as MCA, is to see the method as a way of quantifying categorical data, generalizing the optimal scaling ideas of Chapter 7. As before, there are several equivalent ways to think about MCA as a scaling technique, and these different approaches enrich our understanding of the method’s properties. The optimal scaling approach to MCA is often referred to in the literature as homogeneity analysis .
Data set 11: Attitudes to science and environment . . . . . . . . . . . . 153 Category quantification as a goal . . . . . . . . . . . . . . . . . . . . . . 154 MCA as a principal component analysis of the indicator matrix . . . . . 154 Maximizing inter-item correlation . . . . . . . . . . . . . . . . . . . . . . 155 MCA of scientific attitudes example . . . . . . . . . . . . . . . . . . . . 155 Individual squared correlations . . . . . . . . . . . . . . . . . . . . . . . 156 Loss of homogeneity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 Geometry of loss function in homogeneity analysis . . . . . . . . . . . . 158 Reliability and Cronbach’s alpha . . . . . . . . . . . . . . . . . . . . . . 160 SUMMARY: Scaling Properties of MCA . . . . . . . . . . . . . . . . . . 160
