Subroutines for Maximum Likelihood and Quasi-Likelihood Estimation of Parameters in Nonlinear Regression Models

We present FORTRAN 77 subroutines that solve statistical parameter estimation problems for general nonlinear models, e.g., nonlinear least-squares, maximum likehood, maximum quasi-likelihood, generalized nonlinear least-squares, and some robust fitting problems. Models in the accompanying test examples include members of the nonlinear exponential family ("nonlinear GLIM") and probablistic choice models, such as linear-in-parameter multinomial probit models. The basic method, a generalization of the NL2SOL algorithm for nonlinear least-squares, employs a model/trust-region scheme for computing trial steps, exploits special structure by maintaining a secant approximation to the second-order part of the Hessian, and adaptively switches between a Gauss-Newton and an augumented Hessian approximation.