Suppose that we have a sample of n observations y1, y2, . . . , yn which can be treated as a Poisson distribution, with:
The following variance function:
Furthermore, suppose that we want to let the mean µi (and therefore the variance) depend on a vector of explanatory variables xi. We can adopt a simple linear model of the form:
The linear predictor on the right-hand side of the previous equation can assume any real ...