A beta inflated mean regression model with mixed effects for fractional response variables

• Autor: Fernández Villegas, Renzo
• Formato: tesis de maestría
• Fecha de Publicación: 2017
• Institución: Pontificia Universidad Católica del Perú
• Repositorio: PUCP-Institucional
• Lenguaje: inglés
• OAI Identifier: oai:repositorio.pucp.edu.pe:20.500.14657/144831
• Enlace del recurso: http://hdl.handle.net/20.500.12404/8847
• Nivel de acceso: acceso abierto
• Materia: Estadística bayesiana; Análisis de regresión; Estadística--Modelos matemáticos; https://purl.org/pe-repo/ocde/ford#1.01.03

In this article we propose a new mixed effects regression model for fractional bounded response variables. Our model allows us to incorporate covariates directly to the expected value, so we can quantify exactly the influence of these covariates in the mean of the variable of interest rather than to the conditional mean. Estimation is carried out from a Bayesian perspective and due to the complexity of the augmented posterior distribution we use a Hamiltonian Monte Carlo algorithm, the No-U-Turn sampler, implemented using Stan software. A simulation study for comparison, in terms of bias and RMSE, was performed showing that our model has a better performance than other traditional longitudinal models for bounded variables. Finally, we applied our Beta Inflated mixed-effects regression model to real data which consists of utilization of credit lines in the peruvian financial system.