A beta-inflated mean regression model with mixed effects for fractional response variables

Abstract

In this article we propose a new mixed-effects regression model for fractional bounded response variables. Our model allows us to incorporate covariates directly to the expected value, so we can quantify exactly the influence of these covariates in the mean of the variable of interest rather than to the conditional mean. Estimation is carried out from a Bayesian perspective. Due to the complexity of the augmented posterior distribution, we use a Hamiltonian Monte Carlo algorithm, the No-U-Turn sampler, implemented using the Stan software. A simulation study was performed showing that our model has a better performance than other traditional longitudinal models for bounded variables. Finally, we applied our beta-inflated mean mixed-effects regression model to real data which consists of utilization of credit lines in the peruvian financial system.

Keywords:

• Fractional variables
• proportions
• beta-inflated distribution
• Bayesian inference
• MCMC methods
• Hamiltonian Monte Carlo
• mixed models
• RStan

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Dirección de Gestión de la Investigación at PUCP [DGI-2016-1-0077].