Critérios de seleção e qualidade de ajuste em regressão não linear: uma abordagem de Monte Carlo

Abstract

Nonlinear regression models are widespread in the literature and are widely used mainly for their advantages over linear regression models. Parsimony, applicability and practical interpretatio n of its parameters can be citedas determining factors in the use of these models, which directly reflect in different studies in agriculture, biology, economics, engineering, among others. The use of growth curves is one of the main applications of nonlinear regression models to analyze the development over the life of a certain living being. There are many models in the literature for this purpose, with their unique peculiarities. In order to know which one of these models offer the best fit to the data, different evaluated quality of fit criteria are used, however, there is no way to classify which best criterion for a selection of models should be used in a specific study. Different studies present the coefficient of determination, Akaike’s information criterion, Bayesian information criterion as the most useful for assessing an adjustment and there are some questions regarding its use for the selection of non-linear regression models. Thus, the present study aims to simulate via Monte Carlo four scenarios considering as equations of the logistic non linear regression models, Gompertz, von Bertalanffy and Brody to assess the efficiency of the selection criteria in determining the model that created it generated the data. Four Monte Carlo simulation scenarios were used, each one being considered as standard the logistic models, Gompertz, von Bertalanffy and Brody. Then, 4 models were adjusted for each of the scenarios and the quality assesments most found in the literature were calculated in order to select the appropriate model. The results demonstrate that the asymptotic index, mean absolute deviation and determination coefficient raters show superior efficiency in choosing the appropriate adjustment among the other raters studied for the four simulated scenarios.