Multiple and Joint Correspondence Analysis: Testing the True Dimension of a Study

The problem of the proper dimension of a Multiple Correspondence Analysis (MCA) is discussed, based on both the re-evaluation of the explained inertia sensu Benzécri (1979) and Greenacre (2006) and a test proposed by Ben Ammou and Saporta (1998). This leads to the consideration of a better reconstruction of the off-diagonal sub-tables of the Burt’s table crossing the nominal characters taken into the account. Thus, Greenacre (1988) Joint Correspondence Analysis (JCA) is introduced and the results obtained on two applications are shown. The quality of reconstruction of both MCA and JCA solutions are compared to the Simple Correspondence Analysis results of the two-way tables. It results that JCA’s reduced-dimensional reconstruction is much better than the MCA’s one, that reveals highly biased and non-monotonous