Smoothness of conditional independence models for discrete data

We investigate a family of conditional independence models defined by constraints on complete but non hierarchical marginal log–linear parameters. By exploiting results on the mixed parameterization, we show that these models are smooth when a certain Jacobian matrix has spectral radius strictly less than 1. In the simple context when only two marginals are involved, we prove that this condition is always satisfied. In the general case, we describe an efficient numerical test for checking whether the condition is satisfied with high probability. This approach is applied to several examples of non hierarchical conditional independence models and to a directed cyclic graph model; we establish that they are all smooth.