This chapter deals with the connection between log-linear models for frequencies and multinomial response models for proportions. It focuses on the Poisson distribution for which the sample space is the set of non-negative integers. Under idealized experimental conditions when successive events occur independently and at the same rate, the Poisson model is appropriate for the number of events observed. However, even in well-conducted laboratory experiments, departures from the idealized Poisson model are to be expected for several reasons. The net effect is that the number of recorded events is more variable than the simple Poisson model would suggest. Similarly with the data on ship damage, inter-ship variability leads to over-dispersion relative to the Poisson model. Not all log-linear models are equivalent to multinomial response models and, conversely, not all multinomial response models can be generated from log-linear models.