THE EFFECT OF ASYMMETRIC AND SYMMETRIC DEPENDENCE IN SOME GROWTH MODELS USING COPULAS

Abstract

Growth models are included in non-linear regression models. On the other hand, dependence is one of the most important issues of statistics. Many models have been applied to data and variables which have dependent and correlated. However, the effect of dependence on growth models has not been revealed in researches. Therefore, the aim of this study is to demonstrate the effect of dependence on growth models. Dependence structure can be in the form of asymmetric and symmetric dependence. From this point on, the effect of asymmetric and symmetrical dependence on growth models is shown. For this, a simulation study is considered. In the simulation study, correlated variables are produced by means of Copula functions. The dependence on the variables generated by Copulas is constructed as weak, medium, strong. These levels (weak, medium, strong) of dependence that are constructed in variables have affected the R-squared(R-2) and parameters of growth models. According to the results of simulation study and growth models, in particular, the Von Bertalanffy model has performed better, when the asymmetric dependence is 0.8 (strong-dependence). The Brody model comes into prominence in symmetric dependence 0.8 (strong-dependence), while the Logistic model comes into prominence in symmetric dependence 0.2 (weak-dependence). This study will give researchers remarkable information about which model to apply when working with strong, medium, weak correlated data