Mean regression for (0, 1) responses via beta scale mixtures

Abstract To achieve greater flexibility for modelling heavy-tailed responses on the unit interval, a beta scale mixture (BSM) regression model is proposed. The conditional response is assigned a mean-parameterised beta distribution whose variability parameter is scaled by a mixing random variable, taking values on all or part of the positive real line, whose distribution depends on parameters governing the tail behaviour of the resulting compound distribution. The conditional mean of the response variable is linked to covariates through a logit link, while the mixing mechanism offers greater flexibility towards the skewness and kurtosis than classical beta regression. To validate the effectiveness of the proposed regression model, we conduct a simulation study and illustrate its practical relevance through applications to real datasets. The results indicate that the BSM regression model consistently outperforms the classical beta and alternative competing regression models for responses on the bounded unit domain. The methodology is implemented in the open-source BSMreg package for , available at https://github.com/arnootto/BSM .