Bivariate Model for the Saber 11 Tests in Tolima Department (Colombia)

Résumé 0

In many applications we find data corresponding to variables that are highly correlated, one of them being able to explain the behavior of the others. This happens in particular with the performance in mathematics and critical reading given in the tests SABER11. The theory of copula functions arises as an alternative to measure the dependence of random variables with given marginal distributions, allowing to apply different measures of association and different estimation methods. In this article we show how to build a bivariate model under the context of the Copula functions for data coming from the aforementioned variables. The properties of the adjusted models were verified and different estimation methods were compared such as Kendall's Tau, Spearman's Rho, Pseudo Maximum Likelihood and Maximum Likelihood using the Copula package and VineCopula of the R software in order to verify the quality of the built model. Simulated data were used to carry out this process and the models were applied to real data on performance in critical reading and mathematics for students between 14 and 24 years who presented the tests SABER 11 in 2016 in the Department of Tolima.