Modelo Bayesiano de Teoría de Respuesta al Ítem Multidimensional para datos de naturaleza asimétrica
In the frame of logistic models of Item Response Theory (IRT), it is common to find a hypothesis that states the latent trace line underlying a test can have symmetrical behavior. Nonetheless, in areas such as education, psychology and psychometry, it can be observed that the latent variables may di...
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| Tipo de recurso: | tesis de maestría |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2019 |
| País: | Colombia |
| Institución: | Universidad Nacional de Colombia |
| Repositorio: | Repositorio UN |
| Idioma: | español |
| OAI Identifier: | oai:repositorio.unal.edu.co:unal/75943 |
| Acceso en línea: | https://repositorio.unal.edu.co/handle/unal/75943 |
| Access Level: | acceso abierto |
| Palabra clave: | Teoría de Respuesta al Ítem Item Response Theory Gaussian Copula Bayesian Estimation Asymmetric Distribution Stan Copula Gaussiana Estimación Bayesiana Distribución asimétrica |
| Sumario: | In the frame of logistic models of Item Response Theory (IRT), it is common to find a hypothesis that states the latent trace line underlying a test can have symmetrical behavior. Nonetheless, in areas such as education, psychology and psychometry, it can be observed that the latent variables may display a naturally asymmetric behavior. For instance, neuroticism, which is understood as the capacity to cope with stress and improve the attitude when facing life challenges, is a personality trait that can show a naturally asymmetric behavior, since most of the time the population will respond in a correct or incorrect way to the items of the test requiring this construct, depending on the intention of the items. A multidimensional model of the Item Response Theory is presented, which was created to adjust data from binary or dichotomous tests, which are divided into sub-tests and where the dimension of the trace coincides with the dimension of the test. The model proposed is known as the Multiunidimensional logistic model of the Item Response Theory to the Asymmetric Item of two parameters: MuIRTA-2PL, which mainly considers the asymmetry of the traces and their correlation. Therefore, a Copula Gaussiana, which captures such structure of dependence, is used. Its use is justified since it provides a more adequate adjustment. That is, it recovers and estimates in a better way the incidental and structural parameters of the model, in contrast to the unidimensional model, UIRTA-2PL, Unidimensional Logistic Model of the Response Theory to the Asymmetric Item of two parameters, which is being proposed here, and where the natural asymmetry of the trace is being regarded. The methodology used in this discussion is framed upon the Bayesian Inference principle. In consequence, the Bayesian programming language known as Stan was used, especially the chance to construct functions type, _lpdf (density function), essential when implementing the Multiunidimensional model proposed. Finally, an Inventory test PIHEMA-R2 was used during the admission process to the Faculty of Human Sciences and Education of Universidad Central de Venezuela in 2014. |
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