Bayesian truncated beta nonlinear mixed-effects models

ABSTRACT

Truncated regression models arise in many applications where it is not possible to observe values of the response variable that are above or below certain thresholds. We propose a Bayesian truncated beta nonlinear mixed-effects model by considering the truncated variable to follow a truncated beta distribution. The mean parameter of the distribution is modeled by a nonlinear function of unknown fixed parameters and covariates and by random effects. The proposed model is suitable for response variables, y, bounded to an interval $(a,b)$ without the need to consider a transformed variable $y^{\ast }=(y-a)/(b-a)$ to apply the well-known beta regression model and its extensions, which are primarily appropriate for responses in the interval $(0,1)$. Bayesian estimates and credible intervals are computed based on draws from the posterior distribution of parameters generated using an MCMC procedure. Posterior predictive checks, Bayesian standardized residuals and a Bayesian influence measures are considered for model diagnostics. Model selection is performed using the sum of log-CPO metric and a Bayesian model selection criterion based on Bayesian mixture modeling. Simulated datasets are used for prior sensitivity analysis and to evaluate finite sample properties of Bayesian estimates. The model is applied to a real dataset on soil–water retention.

KEYWORDS:

• Truncated beta distribution
• nonlinear mixed-effects model
• Bayesian inference
• Bayesian diagnostic
• MCMC

Acknowledgments

The authors would like to thank Aline de Holanda Nunes Maia (Empraba, Meio Ambiente) and Lineu Neiva Rodrigues (Embrapa, Cerrados) for supplying the Buruti Vermelho Riven Basin database and for valuable discussion about the experimental data.

The algorithms are available upon request to the corresponding author.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Carolina Costa Mota Paraíba was granted a scholarship by the Brazilian organization Coordenação de Aperfeiçoamento de Pessoal de Nível Superior during this research.