On the maximum likelihood estimation in general log-linear models

General log-linear models specified by non-negative integer design matrices have a potentially wide range of applications, although using models without the genuine overall effect, that is, ones which cannot be reparameterized to include a normalizing constant, is still rare. As shown here, log-linear models without the overall effect arise naturally in practice, and can be handled in a similar manner to models with the overall effect. The properties of the maximum likelihood estimates are discussed in more detail, an iterative scaling procedure for MLE computation is proposed, and its convergence is proved. The results are illustrated using data from a recent clinical study.