  The paper describes a generalized iterative proportional fitting procedure
which can be used for maximum likelihood estimation in a special class of the
general log-linear model. The models in this class, called relational, apply to
multivariate discrete sample spaces which do not necessarily have a Cartesian
product structure and may not contain an overall effect. When applied to the
cell probabilities, the models without the overall effect are curved
exponential families and the values of the sufficient statistics are reproduced
by the MLE only up to a constant of proportionality. The paper shows that
Iterative Proportional Fitting, Generalized Iterative Scaling and Improved
Iterative Scaling, fail to work for such models. The algorithm proposed here is
based on iterated Bregman projections. As a by-product, estimates of the
multiplicative parameters are also obtained.
