ALGORITHM-717 SUBROUTINES FOR MAXIMUM-LIKELIHOOD AND QUASI-LIKELIHOODESTIMATION OF PARAMETERS IN NONLINEAR-REGRESSION MODELS

We present FORTRAN 77 subroutines that solve statistical parameter est imation problems for general nonlinear models, e.g., nonlinear least-s quares, maximum likelihood, maximum quasi-likelihood, generalized nonl inear least-squares, and some robust fitting problems. The accompanyin g test examples include members of the generalized linear model family , extensions using nonlinear predictors (''nonlinear GLIM''), and prob abilistic choice models, such as linear-in-parameter multinomial probi t models. The basic method, a generalization of the NL2SOL algorithm f or nonlinear least-squares, employs a model/trust-region scheme for co mputing trial steps, exploits special structure by maintaining a secan t approximation to the second-order part of the Hessian, and adaptivel y switches between a Gauss-Newton and an augmented Hessian approximati on. Gauss-Newton steps are computed using a corrected seminormal equat ions approach. The subroutines include variants that handle simple bou nds on the parameters, and that compute approximate regression diagnos tics.