A class of statistical models to weaken independence in two-way contingency tables

In this paper we study a new class of statistical models for contingency tables. We define this class of models through a subset of the binomial equations of the classical independence model. We prove that they are log-linear and we use some notions from Algebraic Statistics to compute their sufficient statistic and their parametric representation. Moreover, we show how to compute maximum likelihood estimates and to perform exact inference through the Diaconis-Sturmfels algorithm. Examples show that these models can be useful in a wide range of applications.