  We introduce and study a subclass of joint Bernoulli distributions which has
the palindromic property. For such distributions the vector of joint
probabilities is unchanged when the order of the elements is reversed. We prove
for binary variables that the palindromic property is equivalent to zero
constraints on all odd-order interaction parameters, be it in parameterizations
which are log-linear, linear or multivariate logistic. In particular, we derive
the one-to-one parametric transformations for these three types of model
specifications and give simple closed forms of maximum likelihood estimates.
Some special cases and a case study are described.
