Regression Models Used in Food Science: Linearity, Reparameterization, and Rescaling

Abstract

Models can be linear or nonlinear; however, the linearity of a model refers to its parameters. Although linear regression has several advantages over nonlinear regression such as having an analytical solution and symmetric confidence intervals, most regression models used in food science are nonlinear. Therefore, nonlinear regression should be used to obtain the parameters and their uncertainties. Reparameterization can be useful to have interpretable parameters, and sometimes it is better to perform nonlinear regression instead of simple linear regression even if there is a linear relationship between the dependent and independent variable. Rescaling is a desirable method to have statistically significant parameters. The aim of this paper is to discuss the linearity of the models and to show some useful reparameterization and rescaling by using some published data. Examples are given from food microbiology (microbial inactivation kinetics) and degradation kinetics of foods.