Maximum Likelihood and Quasi-Likelihood for Nonlinear Exponential Family Models

Linear and nonlinear exponential family and quasi-likelihood regression models form a class of models exhibiting a common structure that invites using one algorithmic framework to compute parameter estimates and regression diagnostics for all members in the class. This framework extends our work on nonlinear least squares; it includes iteratively reweighted least squares, but also encompasses secant updates for a piece of the Hessian matrix of the likelihood or quasilikelihood function along with adaptive decisions about when to use this information.