Error analysis in predictive modelling demonstrated on mould data.

The purpose of this paper was to develop a predictive model for the effect of temperature and water activity on the growth rate of Aspergillus niger and to determine the sources of the error when the model is used for prediction. Parallel mould growth curves, derived from the same spore batch, were generated and fitted to determine their growth rate. The variances of replicate ln(growth-rate) estimates were used to quantify the experimental variability, inherent to the method of determining the growth rate. The environmental variability was quantified by the variance of the respective means of replicates. The idea is analogous to the "within group" and "between groups" variability concepts of ANOVA procedures. A (secondary) model, with temperature and water activity as explanatory variables, was fitted to the natural logarithm of the growth rates determined by the primary model. The model error and the experimental and environmental errors were ranked according to their contribution to the total error of prediction. Our method can readily be applied to analysing the error structure of predictive models of bacterial growth models, too.