Bayesian beta nonlinear models with constrained parameters to describe ruminal degradation kinetics

TL;DR

This paper introduces a Bayesian beta nonlinear model with constrained parameters for more accurate ruminal degradation kinetics, overcoming limitations of traditional least squares methods and providing a practical, generalizable approach.

Contribution

It proposes an objective prior distribution method for complex nonlinear models with constrained parameters, applicable in Bayesian analysis and implemented in OpenBUGS.

Findings

The Bayesian beta model outperformed traditional methods in prediction accuracy.

The model demonstrated good coverage of credible intervals in simulations.

Application to real data showed improved model fit using Deviance Information Criterion.

Abstract

The models used to describe the kinetics of ruminal degradation are usually nonlinear models where the dependent variable is the proportion of degraded food. The method of least squares is the standard approach used to estimate the unknown parameters but this method can lead to unacceptable predictions. To solve this issue, a beta nonlinear model and the Bayesian perspective is proposed in this article. The application of standard methodologies to obtain prior distributions, such as the Jeffreys prior or the reference priors, involves serious difficulties here because this model is a nonlinear non-normal regression model, and the constrained parameters appear in the log-likelihood function through the Gamma function. This paper proposes an objective method to obtain the prior distribution, which can be applied to other models with similar complexity, can be easily implemented in OpenBUGS, and solves the problem of unacceptable predictions. The model is generalized to a larger class of models. The methodology was applied to real data with three models that were compared using the Deviance Information Criterion and the root mean square prediction error. A simulation study was performed to evaluate the coverage of the credible intervals.