Binomial regression models with a flexible generalized logit link function

In binomial regression, a link function is used to join the linear predictor variables and the expectation of the response variable. This paper proposes a flexible link function from a new class of generalized logistic distribution, namely a flexible generalized logit (glogit) link. This approach considers both symmetric and asymmetric models, including the cases of lighter and heavier tails, as compared to standard logistic. The glogit is created from the inverse cumulative distribution function of the exponentiated-exponential logistic (EEL) distribution. Using a Bayesian framework, we conduct a simulation study to investigate the model performance compared to the most commonly used link functions, e.g., logit, probit, and complementary log-log. Furthermore, we compared the proposed model with several other asymmetric models using two previously published datasets. The results show that the proposed model outperforms the existing ones and provides flexibility fitting the experimental dataset. Another attractive aspect of the model are analytically tractable and can be easily implemented under a Bayesian approach.