Zero- and/or One-Augmented Flexible Beta Regression with EM-Based Estimation

Proportion data frequently arise in applied studies and are commonly modeled using beta regression when responses lie in the open unit interval (0, 1). However, real datasets often include observations equal to zero and/or one, which standard beta-based models are unable to accommodate. Building on the flexible beta (FB) distribution, which extends the beta distribution by allowing greater flexibility in the shape of the density, this work proposes a zero- and/or one-augmented FB regression model. This model assigns positive probability mass to the boundaries of the support while preserving the parametric structure of the FB distribution. Parameter estimation is carried out through an expectation–maximization algorithm derived from a finite mixture representation of the model. The proposed approach is illustrated through an application to a real dataset in the context of video game engineering, and its predictive performance is assessed using standard accuracy measures.