A0292
Title: The Cressie-Read divergence statistic and correspondence analysis; a unifying approach with possible extensions
Authors: Eric Beh - University of Newcastle (Australia)
Rosaria Lombardo - University of Campania (Italy) [presenting]
Abstract: In the correspondence analysis literature, the foundations of visually and numerically summarising the association between two categorical variables rest with Pearson's chi-squared statistic. Not only is this statistic extremely popular and versatile, but it also yields some very useful visual and numerical properties. More recently, ties have been established that show the role that the Freeman-Tukey statistic plays in correspondence analysis and confirmed the advantages of the Hellinger distance that have long been advocated. Both Pearson's and the Freeman-Tukey statistics are special cases of the Cressie-Read divergence statistic, as are the Cressie-Read statistic, the likelihood ratio statistic and their modified versions. Therefore, correspondence analysis will be explored where the association, and the resulting low-dimensional correspondence plot, have at its foundation this divergence statistic. By doing so, the properties of correspondence analysis are described for any special case of the Cressie-Read divergences statistic which includes the Hellinger distance decomposition (HDD) method and log-ratio analysis (LRA). Some extensions to this method will also be discussed including its role in multiple and multi-way correspondence analysis.
