In this lesson, we showed how the generalized linear model can be applied to count data, using the Poisson distribution with the log link. Compared with the logistic regression model, two differences we noted are the option to use the negative binomial distribution as an alternate random component when correcting for overdispersion and the use of an offset to adjust for observations collected over different windows of time, space, etc. Much of the properties otherwise are the same (parameter estimation, deviance tests for model comparisons, etc.).
One other common characteristic between logistic and Poisson regression that we change for the log-linear model coming up is the distinction between explanatory and response variables. The log-linear model makes no such distinction and instead treats all variables of interest together jointly. This allows greater flexibility in what types of associations can be fit and estimated, but one restriction in this model is that it applies only to categorical variables.