Variability of growth parameter estimates - The role of rescaling and reparametrization

The focus of this paper is to analyze the reliability of the error estimation when well-known primary models of predictive microbiology are used to fit growth parameters. We also demonstrate the application of rescaling and reparametrization to improve this reliability. We highlight that the technique can be useful for achieving linearity and homoscedasticity, reducing the complexity of the model, generating initial parameter estimates when fitting experimental data by non-linear regression, and obtaining realistic standard errors for the parameter estimates, which are crucial for decision-making in food safety. We classify the sources of the total variability and correlation of the parameter estimates as "wet" and "dry". We point out that, rescaling and reparametrization do not change the model in a mechanistic sense but they can reduce the variances of (and/or the correlation between) the parameter estimates, thus mitigate the effects of such "dry" (i.e. statistical) relationships. We analyze the reliability of the error estimation when the model of Baranyi and Roberts (BRM) and the Gompertz function (GF) are used to fit data. The comparison is based on the distribution of the standard error of the maximum specific growth rate estimates. The results show that the error structure of the BRM-fit is closer to that of the linear regression, making BRM more reliable for constructing confidence intervals by conventional means, using the t-distribution assumption for the parameter estimates.