Bivariate Model for the Saber11 Tests in Tolima Department (Colombia)
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 varia...
| Main Authors: | , , |
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| Format: | Online |
| Language: | spa |
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Universidad Pedagógica y Tecnológica de Colombia
2019
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| Subjects: | |
| Online Access: | https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/8561 |
| _version_ | 1801706343684374528 |
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| author | Garcia saavedra, Yuri Marcela Clavijo Mendez, Jairo Alfonso Luugo Capera, Oscar Andres |
| author_facet | Garcia saavedra, Yuri Marcela Clavijo Mendez, Jairo Alfonso Luugo Capera, Oscar Andres |
| author_sort | Garcia saavedra, Yuri Marcela |
| collection | OJS |
| description | 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. |
| format | Online |
| id | oai:oai.revistas.uptc.edu.co:article-8561 |
| institution | Revista Ciencia en Desarrollo |
| language | spa |
| publishDate | 2019 |
| publisher | Universidad Pedagógica y Tecnológica de Colombia |
| record_format | ojs |
| spelling | oai:oai.revistas.uptc.edu.co:article-85612020-11-11T02:06:49Z Bivariate Model for the Saber11 Tests in Tolima Department (Colombia) Modelo Bivariado para las Pruebas Saber11 en el Departamento Del Tolima (Colombia) Garcia saavedra, Yuri Marcela Clavijo Mendez, Jairo Alfonso Luugo Capera, Oscar Andres Modelos bivariados, funciones cópula, dependencia entre variables aleatorias Bivariate models, copula functions dependence between random variables. 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. En muchas aplicaciones encontramos datos que se restringen al intervalo (0;1), tales como porcentajes y proporciones, y que además pueden ser explicados por otras variables a través de un modelo de regresión en el que la variable respuesta está distribuida como una beta. Por otro lado, se encuentran pares de variables que tienen cierta dependencia como es el caso del rendimiento en matemáticas y lectura crítica dados en las pruebas saber11 en el departamento del Tolima (Colombia) 2016. La teoría de las funciones cópula surgen como una alternativa para medir la dependencia de variables aleatorias con distribuciones marginales dadas, permitiendo estimar diferentes medidas de asociación y diferentes métodos de estimación. En este artículo se usó un Modelo Bivariado bajo el contexto de las funciones Cópula para datos que están en el intervalo (0;1). Se verificaron las propiedades de los modelos ajustados y se compararon diferentes métodos de estimaciones usando el paquete Cópula y VineCopula del software R con el fin de establecer cuál es el mejor. Se usaron datos simulados para realizar este proceso y se aplicaron los modelos a datos reales de rendimiento en lectura crítica y matemáticas en estudiantes entre los 14 a 24 años. Universidad Pedagógica y Tecnológica de Colombia 2019-07-23 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion text English application/pdf https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/8561 10.19053/01217488.v10.n2.2019.8561 Ciencia En Desarrollo; Vol. 10 No. 2 (2019): Vol 10, Núm. 2 (2019): Julio - Diciembre; 169-176 Ciencia en Desarrollo; Vol. 10 Núm. 2 (2019): Vol 10, Núm. 2 (2019): Julio - Diciembre; 169-176 2462-7658 0121-7488 spa https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/8561/8648 |
| spellingShingle | Modelos bivariados, funciones cópula, dependencia entre variables aleatorias Bivariate models, copula functions dependence between random variables. Garcia saavedra, Yuri Marcela Clavijo Mendez, Jairo Alfonso Luugo Capera, Oscar Andres Bivariate Model for the Saber11 Tests in Tolima Department (Colombia) |
| title | Bivariate Model for the Saber11 Tests in Tolima Department (Colombia) |
| title_alt | Modelo Bivariado para las Pruebas Saber11 en el Departamento Del Tolima (Colombia) |
| title_full | Bivariate Model for the Saber11 Tests in Tolima Department (Colombia) |
| title_fullStr | Bivariate Model for the Saber11 Tests in Tolima Department (Colombia) |
| title_full_unstemmed | Bivariate Model for the Saber11 Tests in Tolima Department (Colombia) |
| title_short | Bivariate Model for the Saber11 Tests in Tolima Department (Colombia) |
| title_sort | bivariate model for the saber11 tests in tolima department colombia |
| topic | Modelos bivariados, funciones cópula, dependencia entre variables aleatorias Bivariate models, copula functions dependence between random variables. |
| topic_facet | Modelos bivariados, funciones cópula, dependencia entre variables aleatorias Bivariate models, copula functions dependence between random variables. |
| url | https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/8561 |
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