An Introduction to Correspondence Analysis. Eric J. Beh

in terms of a particular data or area of research. Michael Greenacre’s book Correspondence Analysis in Practice, which is now in its third edition (as of 2017) provides an excellent introductory description of correspondence analysis. Despite the excellent discussion of a wide range of topics, his book focuses on nominal categorical variables and so deals with the more traditional approaches to performing correspondence analysis.

      What makes this book distinctive is that we don’t just introduce how to perform correspondence analysis for two or more nominal categorical variables using the traditional techniques. This book also provides some introductory remarks on the theory and application of non-symmetrical correspondence analysis; a variant that accommodates for a predictor variable and a response variable. We also provide an introduction to how ordered categorical variables can be incorporated into the analysis. For the analysis of multiple nominal categorical variables we do give an introduction to the classical approaches to multiple correspondence analysis (which involve transforming a multi-way contingency table into a two-way form) but we also provide some introductory remarks and an application of multi-way correspondence analysis; a technique which preserves the hyper-cube format of a multi-way contingency table. For the sake of simplicity though, we restrict our attention to the analysis of three variables, but we do examine how to analyse their association when two of them are treated as a predictor variable and the third variable is treated as a response variable.

      The one omission from this book is that we do not discuss multi-way correspondence analysis when some of the variables are ordered and some of them are nominal. We could certainly have included some introductory notes on how to perform such an analysis but we felt it was slightly beyond the scope of what we wanted to achieve with this introductory book.

      Another point that we would like to make concerns the use of two terms we have used; association and interaction. We use association to refer to the general relationship that exists between two (or more) categorical variables while interaction describes the relationship between two (or more) specific categories from two (or more) variables.

      Therefore, this book aims to help researchers improve their familiarity with the concepts, terminology and application of several variants of correspondence analysis. We do describe the theory underlying the statistical and more visual aspects of the analysis. We have also tried to make sure that this book reaches out to students and educators who wish to learn (and teach) the fundamentals of correspondence analysis. In particular, the introductory nature of this book should enable students enrolled in an honours degree (for those in countries such as, but not confined to, Australia, New Zealand, United Kingdom, Canada, Hong Kong and India), a masters program or a PhD in all fields of research to gain appreciation of this form of analysis. The only requirement we ask of the reader is to have some knowledge of introductory statistics. To help the reader, all of the techniques we described can be performed using three R packages that are available on the CRAN; these packages are CAvariants , MCAvariants and CA3variants . However, to avoid an overly long book, we have not provided any guidance on how these packages may be used (reckonizing that they will be constantly updated), although one may refer to their help files for guidance and insight into their use.

      So, sit back, relax, and we hope you enjoy your journey into the world of correspondence analysis.

       April 2020

      Eric J. Beh

       Newcastle, Australia

      Rosaria Lombardo

       Capua, Italy