I would like to ask you about Correspondence Analysis.

I am wondering if does any strategy exist to test the significance of the groupings revealed by CA. I understand that chi-square test can be applied to verify if a statistical significant association exist between rows and columns (taking into account the total inertia multiplied by the sample-size, and the associated degree of freedom).

This informs us about the overall association.

But, moving from a exploratory framework to a hypothesis testing perspective, how can one pinpoint which profiles are significantly different in a statistical sense (e.g., to test if a clustering can be considered significant).

I have read Greenacre, "Correspondence Analysis in Practise" (2008), Chapter 15. He interestingly talk about Ward clustering performed on the basis of rows/columns profile and associated masses. I would like to know if did anyone performed this approach?

Any comment on the general issue, or on the aforementioned reference and related technique, is welcome.

Thank you

Kind regards and happy new year

Gianmarco