We consider the statistical problem of analyzing the association between two categorical variables from cross-classified data. The focus is put on measures which enable one to study the dependencies at a local level and to assess whether the data support some more or less strong association model. Statistical inference is envisaged using an imprecise Dirichlet model. Keywords association, logical model, directional association model, statistical inference, upper and lower probabilities, IDM, prior ignorance, Bayesian inference