Representing interaction in multiway contingency tables: MIDOVA, CA and log-linear model.
Martine Cadot, Alain Lelu · 2011
Correspondence Analysis (CA) is particularly suited to categorical variables, as long as 2-way contingency tables are concerned. (Mourad 1983) has pointed out that its extension to 3-way contingency tables is far from trivial, due to interaction effects between the variables. (Escofier 1983) has provided a non-symmetric solution to this problem, through the example of a 3-way qualification×profession×gender table, disregarding interaction in this first approach. Then (Escofier & Pagès 1988) took interaction into account, still in a non-symmetric scheme, and illustrated with the same example, and in (Abdessemed & Escofier 2000) this CA approach was contrasted with the log-linear model one. Beside CA and log-linear model, issued from the statistics domain, other research streams originating in Artificial Intelligence have coped with the same problem: we will present here the extension to categorical variables of our results on extracting and statistically validating « itemsets » in boolean datatables, results first published in (Cadot 2006) – for a survey on itemset approaches, see (Han 2001). We coined MIDOVA (Multidimensional Interaction Differential of Variation) our method for highlighting and representing complex links between qualitative variables, which includes interaction, well-suited to socio-economic data (Haj Ali & Cadot 2010). We will compare it to the CA and log-linear model approaches, using the same 3-way example as Escofier and her colleagues. We will show that out method is effective for general N-way interactions (N may be far greater than