Efficiency comparison of objective function definition for the parameter regression in nonlinear models

An inside-variance estimation method (IVEM) for nonlinear regression is compared with more typical regression approaches such as Least Squares Minimization (LSM) and traditional Maximum Likelihood (ML). This maximum likelihood method involves the re-computation of the variance between the experimental data and predicted data using the regressed parameters. This calculation is done for each of the iterations of the optimization procedure, automatically re-weighting the objective function.{09}Most of the maximum likelihood approaches currently used to regress the parameters of nonlinear models fix the variances, converting the problem into a traditional weighted least squares minimization. However, such approaches lead to residual variances that are inconsistent with the weights and, consequently may not produce the best or most likely parameters according to the model and objective functions used.; From the analysis presented in this work using two kinetic models, the IVEM method performs better under uncertain conditions than traditional Maximum Likelihood and Least Squares Minimization. In all the cases, the three methods fit the experimental data very well. However, the IVEM procedure often found parameter values that were of superior quality for extrapolating than the other two methods.