Evaluation of non-linear and mixed non-linear models to describe in vitro gas production kinetics of ruminant feeds

Abstract

The performance of non-linear and mixed non-linear models was evaluated in the description of in vitro gas production kinetics of ruminant feeds. For this, the logistic, Gompertz and Groot models were used. The analyzes included the addition of random effects to the asymptotic parameter of each model, since this parameter was the one that varied the most among the incubation bottles. Each random effect was associated with a probable source of variability in the experiment. The parameters were estimated with the NLMIXED proc of SAS program. For the selection of the best fit model, the R2aj, σ2, AIC and BIC were considered. In addition, compliance with the basic assumptions for the residuals and the relationship among mathematical fit, simplicity and biological interpretation of the parameters were assessed. It is concluded that the non-linear mixed models allowed to obtain better R2aj, BIC and σ2. The random effects had no significant effect on the fulfillment of the assumptions of autocorrelation and randomness of residuals. The random effect bottle over time allowed to determine the times in which there was a lack of fit. Despite the limitations of the analyzed models, the logistic, without the inclusion of the random effect, was the most appropriate according to the parsimony criterion.
Keywords: mathematical modeling, random effect, goodness of fit, parsimony, fermentation