Sensibility analysis of homogeneity tests of in vitro gas production curves by Monte Carlo simulation

Abstract

In order to improve the ruminant feed evaluation techniques through a statistical method permitting the comparison of treatments in experiments of in vitro gas production, based on regression curves, data were collected from an experiment of in vitro gas production. The Gompertz function was fitted and the Monte Carlo simulation method was used, with the aim of analyzing the sensibility of four homogeneity tests of non-linear regression models. Thirteen new treatments were obtained, with 300 repetitions each and 280 points simulated per each repetition. The homogeneity tests were: extra sum of squares, Bayesian information criterion (BIC), Akaike information criterion (AIC), and Akaike information criterion corrected (AICC). The comparison criteria were assessed with modifications to the parameters, on the order of 1, 3, 5, and 10 %. The methodology for the comparison of the curves was based on the definition of the complete and the reduced models. The sensibility of each method was established according to the probability of fulfillment of the null hypothesis. The AICC showed higher sensibility, followed by the test of extra sum of squares. The AIC and the BIC were the least sensible. The parameter that affected the most the differences between treatments was the asymptotic coefficient (A).