Beside CA and log-linear model, issued from the statistics domain, other research streams originating in Artificial Intelligence have coped with the interacting variables problem: we will present here the extension to categorical variables of our results on extracting and statistically validating " itemsets " in boolean datatables. 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. 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 3), whether symmetrically or not, and results both in easy and detailed interpretability, as CA does, and in statistical significance testing, as the log-linear model does in the case of few variables.