Alternative models for describing biological variables with non-normality and non-linear performance. Study case

Abstract

Alternative models, which do not follow a normal distribution or have linear performance, were examined to describe biological variables such as in vitro gas production. Two analyses were performed: the first ignored the lack of normality of the response variable, while the second considered the non-compliance with this assumption. Parameter estimation was performed using the NLMIXED procedure. The following statistical criteria were used to select the model with the best goodness of fit: CME, R²aj, AIC, BIC, and parameter significance. The fulfillment of the hypotheses of independence and randomness of the residual component was also considered. The tests to select the probability distribution of in vitro gas production showed that it has an exponential distribution (P>0.05). It is concluded that the logistic model with a “log” link function to estimate the population mean of in vitro gas production did not show adequate results. However, the segmental linear model was the one that best described this performance, revealing the best R²aj, CME, AIC, BIC and visually random residuals. Also, with the segmental linear model similar results were obtained, regardless of the normality of the response variable. The results showed that in certain cases parametric procedures can be used with data that do not fulfill with normality. However, the consequences of such violations must be taken into account. A segmental linear model is proposed as an alternative to describe in vitro gas production when the data do not fulfill with normality.