Diagnóstico e seleção de modelos com resposta binária e função de ligação assimétrica - Coelho, Fabiano Rodrigues (2023)
For binary response variables, probit and logit link functions are widely used. However, when the data is imbalanced, traditional approaches may not be suitable. In this thesis, we consider the skew-probit link function as a potential alternative for models with binary response. The parameters are estimated through a Bayesian approach using Hamiltonian Monte Carlo, and residual analysis is developed. Additionally, an extension for the case of mixed models is presented, with parameter estimation performed through numerical integration. As a practical application, we analyze two datasets. In both applications, it is possible to observe, through model selection criteria, that the skew-probit regression model is more efficient than traditional approaches. Computationally, for the fixed-effects model, we use the Stan language adapted to the R software. In the mixed case, the INLA methodology is considered. Proposals for future research are also discussed.