Utilitarian Comparison of Nonlinear Regression Methods

Abstract

To overcome the shortcomings of the least squares regression method, two methods - the normal distance, and the maximum likelihood, were developed. The maximum likelihood is a more generic method, with the normal distance being a consequence of it when error variances in the input and output measurements are equal. The methods were compared with the least squares method through Monte Carlo simulations for Titration and Packed Bed Reactor models. The methods were tested for varying magnitudes of uncertainty, for a sufficient number of realizations to ensure the results reflected the average parameter estimates, and were unique to the regression method. The results for the maximum likelihood method were found to be at par with the best method in most cases. The vertical and the normal distance method had individual preferences depending upon the relative magnitudes of uncertainty. However the programming burden for the maximum likelihood and the normal distance method, apart from the estimate of uncertainty variances for the maximum likelihood method, were the drawbacks. But, approximate estimate of the variances for the maximum likelihood method also yielded good results, as tested for a few cases. Hence for a more accurate estimate of regression parameters, the maximum likelihood method could be adopted with a higher probability of getting the desired results as compared to the other two methods.