Bayesian modeling of the Gompertz curve for meat quails growth data considering different error distributions

This study applied the Gompertz model to quail growth data, assuming symmetric and asymmetric homoscedastic and heteroscedastic error distributions (Normal, t-Student, Skew normal, and Skew t), undera Bayesian framework. Model selection criteria included the Bayesian Deviance Information Criterion (DIC) and the analysis of residual standard deviation (σ), as well as graphical assessment of the fit. For both homoscedastic error structures (males: DIC=7.186; σ=10.73) and (females: DIC=5.572; σ=11.88) as well as heteroscedastic structures (males: DIC=6.493; σ=0.795) and (females: DIC=4.405; σ=0.824), the best fits were obtained by considering the Skew t distribution for errors. In homoscedastic fits, significant residual asymmetry (λ) was observed only for female quails (CI(λ)=[-8.039;-0.340]), whereas in heteroscedastic fits, the parameter was not significant for both sexes. Additionally, heteroscedasticity (δ) captured in the fits was significant for both sexes (males: CI(δ)=[1.66;2.13] and females: CI(δ)=[1.80;2.26]). Understanding animal growth is crucial for optimizing management and feeding practices, reducing time and costs in production. In this case, the use of nonlinear models considering heteroscedastic and/or asymmetric residual structures contributes to greater accuracy in decision-making.