MLGA: A SAS Macro to Compute Maximum Likelihood Estimators via Genetic Algorithms

Abstract

Nonlinear regression is usually implemented in SAS either by using PROC NLIN or PROC NLMIXED. Apart from the model structure, initial values need to be specified for each parameter. And after some convergence criteria are fulfilled, the second order conditions need to be analyzed. But numerical problems are expected to appear in case the likelihood is nearly discontinuous, has plateaus, multiple maxima, or the initial values are distant from the true parameter estimates. The usual solution consists of using a grid, and then choosing the set of parameters reporting the highest log-likelihood. However, if the amount of parameters or grid points is large, the computational burden will be excessive. Furthermore, there is no guarantee that, as the number of grid points increases, an equal or better set of points will be found. Genetic algorithms can overcome these problems by replicating how nature optimizes its processes. The MLGA macro is presented; it solves a maximum likelihood estimation problem under normality through PROC GA, and the resulting values can later be used as the starting values in SAS nonlinear procedures. As will be demonstrated, this macro can avoid the usual trial and error approach that is needed when convergence problems arise. Finally, it will be shown how this macro can deal with complicated restrictions involving multiple parameters.