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. In this paper we propose a Bayesian truncated beta nonlinear mixed-effects model, assuming that the truncated response variable follows a truncated beta distribution and that its location parameter is parametrized by a nonlinear continuous and twice differentiable function of unknown fixed parameters and covariates and by random effects. The proposed model is suitable for any response variable, y, bounded to an interval (a, b) without the need to consider a rescaled variable y * = (y − a)/(b − a) to apply the well known beta regression model and its extensions, which are primarily suitable for response variables in the unit interval (0, 1). Bayesian estimates and credible intervals are computed based on draws from the posterior distribution of parameters obtained using an MCMC procedure. Posterior predictive checks, Bayesian standardized residuals and a Bayesian influence measures are considered to check model adequacy, outliers and influential observations. For model selection, we consider the sum of log-CPO metric and a Bayesian model selection criteria based on Bayesian mixture modeling. Simulated datasets are used for prior sensitivity analysis and to assess frequentist properties of Bayesian estimates and a real dataset on soil-water retention is analyzed.