In linear regression, we saw an equation of the form:
In Poisson Regression, the response variable Y is a count or rate (Y/t) that has a Poisson distribution with expected (mean) count of as , which is equal to variance.
In case of logistic regression, we would probe for values that can maximize log-likelihood to get the maximum likelihood estimators (MLEs) for coefficients.
There are no closed-form solutions, hence the estimations of maximum likelihood would be obtained using iterative algorithms such as Newton-Raphson and Iteratively re-weighted least squares (IRWLS).
Poisson regression is suitable for the count-dependent variable, which must meet the following guidelines:
It follows a Poisson distribution
Counts are not negative
Values are whole numbers (no fractions)