Author Information

William J. Price
Bahman Shafii

Abstract

Biological research data are often represented using nonlinear model specifications that lend themselves to the testing of relevant hypotheses concerning the model parameters. This is typically achieved with classical nonlinear least squares techniques such as Gauss-Newton or Levenberg-Marquardt which allow for both the estimation and inference phases of the analysis. Under some circumstances, however, sensitivity to data or model specifications may lead these methods to fail convergence tests or exhibit nonlinearity in the parameter estimates, which will in turn limit the usefulness of inferential results. In such cases, other estimation methods may present a means of avoiding these problems while providing analogous results. The genetic algorithm combined with bootstrapping and Bayesian estimation are two such alternatives. Genetic algorithms represent a nonparametric approach which, when augmented with bootstrap methods, result in both parameter estimation and approximation of the distribution(s). Bayesian estimation, on the other hand, leads directly to parameter distribution and achieves the required moments. These methods and classical nonlinear least squares are demonstrated utilizing a four- parameter cumulative Wei bull function fitted to onion seed germination data.

Keywords

Least Squares Estimation, Genetic Algorithm, Bayesian Techniques

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Apr 27th, 8:45 AM

ALTERNATIVE PROCEDURES FOR ESTIMATION OF NONLINEAR REGRESSION PARAMETERS

Biological research data are often represented using nonlinear model specifications that lend themselves to the testing of relevant hypotheses concerning the model parameters. This is typically achieved with classical nonlinear least squares techniques such as Gauss-Newton or Levenberg-Marquardt which allow for both the estimation and inference phases of the analysis. Under some circumstances, however, sensitivity to data or model specifications may lead these methods to fail convergence tests or exhibit nonlinearity in the parameter estimates, which will in turn limit the usefulness of inferential results. In such cases, other estimation methods may present a means of avoiding these problems while providing analogous results. The genetic algorithm combined with bootstrapping and Bayesian estimation are two such alternatives. Genetic algorithms represent a nonparametric approach which, when augmented with bootstrap methods, result in both parameter estimation and approximation of the distribution(s). Bayesian estimation, on the other hand, leads directly to parameter distribution and achieves the required moments. These methods and classical nonlinear least squares are demonstrated utilizing a four- parameter cumulative Wei bull function fitted to onion seed germination data.