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The impact of power transformations to rec​​​iprocal averaging, canonical correlation analysis and correspondence analysis

Eric Beh and Rosaria Lombardo 

The role of transformations has gained wide attention in the correspondence analysis literature. In particular, the focus of such transformations have focused on the profiles of a two-way contingency table and is largely due to the impact of the work undertaken by Michael Greenacre over a decade ago. While his work examined on the impact of a power transformation of the elements of a contingency table and of a profile, the results from this approach can also be obtained by considering the same power transformations from a reciprocal averaging and canonical correlation perspective. A few questions arise though. For example, what possible range of transformations exist that ensure that the correspondence analysis is depicting the association between categorical variables that remains statistically significant? Also, what happens if transformations other than a power transformation – such as a log transformation or a trigonometric transformation are considered? This projects expands the role of power transformations in correspondence analysis and its related areas, including the impact of such transformations on the interpretation of the resulting low-dimensional visualisations that can be obtained from them.​