Likelihood Function

Let be a link function such that

where is a column vector for regression coefficients. The pseudo-log likelihood is

Denote the pseudo-estimator as , which is a solution to the estimating equations:

where is the matrix of partial derivatives of the link function with respect to .

To obtain the pseudo-estimator , the procedure uses iterations with a starting value for . See the section Iterative Algorithms for Model Fitting for more details.