Non-Linear Regression Algorithms for Selected Growth Models

Abstract

For the optimization process to start, traditional statistical methods for nonlinear regression models need a starting point (initial parameters or guess values). The parameters must first be predicted using an iterative process after the nonlinear regression model expression has been written, the parameter names have been expressed, and the initial parameter values have been defined. The Gauss-Newton and Levenberg-Marquardt methods (algorithms) for solving non-linear regression models were used in a computer program for predicting three growth models (Logistic, Gompertz, and Weibull models). The multiplicative error terms used to decompose the growth models help specify the best algorithm and model for growth studies. Before using an iterative approach, second-order regression techniques were used to solve the problem of the initial parameters. The final estimate of the parameters, standard errors, p-values, and model adequacy metrics like (R2, Adj. R2, MSE, SSE, AIC, and BIC) that were used to select the best algorithm and growth model are displayed in the result. The Weibull Growth Model with Multiplicative Error Terms was determined to be the ideal growth model by this study. The Gauss-Newton Algorithm was once again found to be the best algorithm for solving nonlinear regression models in this study. Finally, this study suggest/recommend using the Gauss-Newton algorithm to solve non-linear regression models and the Weibull Growth Model for additional growth studies.