Modelling two way contingency tables with recursive logits and odds ratios

In this work a new type of logits and odds ratios, which includes as special cases the continuation and the reverse-continuation logits and odds ratios, are defined. We prove that these logits and odds ratios define a parameterization of the joint probabilities of a two way contingency table. The problem of testing equality and inequality constraints on these logits and odds ratios is examined with particular regard to two new hypotheses of monotone dependence. Work partially supported by a MIUR2004 grant. Preliminary findings have been presented at SIS (Società Italiana di Statistica) Annual Meeting, Torino, 2006.