Bivariate Model for the Saber11 Tests in Tolima Department (Colombia) (2019)
In many applications, we find data that are restricted to belong to the interval (0;1), such as percentages and proportions, which also can be explained by other variables by means of a regression model in which the response variable has beta distribution. On the other hand, there are pairs of variables that have some dependency, such as math and language performance in the state test Saber11 in Tolima Department (Colombia) in 2016. The theory of Copula functions arises as an alternative to measure the dependence of random variables with given marginal distributions, allowing to estimate different measures of association and to construct different methods of estimation. To analyze this type of data, we use a bivariate model under the context of copula functions for data in the interval (0;1). Properties of fitted models were verified, and different estimation methods, were compared using the copula and VineCopula packages of the R software in order to establish the best model for analyzing this type of data. Simulated data were used to carry out this process, and the models were applied to real data of performance in critical reading and mathematics of students between 14 and 24 years.