Mathematical Formalization and Applications to Data with Excess of Zeros and Ones of the Unit-Proportional Hazard Inflated Models

Abstract

In this study, we model the rate or proportion of a specific phenomenon using a set of known covariates. To fit the regression model, which explains the phenomenon within the intervals (0,1), [0,1), (0,1], or [0,1], we employ a logit link function. This approach ensures that the model’s predictions remain within the appropriate range of zero to one. In cases of inflation at zero, one, or both, the logit link function is similarly applied to model the dichotomous Bernoulli-type variable with a multinomial response. The findings demonstrate that the model yields a non-singular information matrix, ensuring valid statistical inference. This ensures the invertibility of the information matrix, allowing for hypothesis testing based on likelihood statistics regarding the parameters in the model. This is not possible with other asymmetric models, such as those derived from the skew-normal distribution, which has a singular information matrix at the boundary of the skewness parameter. Finally, empirical results show the model’s effectiveness in analyzing proportion data with inflation at zero and one, proving its robustness and practicality for analyzing bounded data in various fields of research.