Algorithm 717: Subroutines for maximum likelihood and quasi-likelihood estimation 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 likelihood, maximum quasi-likelihood, generalized nonlinear least squares, and some robust fitting problems. The accompanying test examples include members of the generalized linear model family, extensions using nonlinear predictors (“nonlinear GLIM”), and probabilistic 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 augmented Hessian approximation. Gauss-Newton steps are computed using a corrected seminormal equations approach. The subroutines include variants that handle simple bounds on the parameters, and that compute approximate regression diagnostics. (Source:

This software is also peer reviewed by journal TOMS.