Theil error splitting method for selecting the "best model" in microbial inactivation studies

Escherichia coli K-12 was grown under unbuffered, buffered, and starving environmental conditions and then subjected to isothermal inactivation at 58°C for up to 30 min. Survival versus time data were used to evaluate three models reported as suitable for the prediction of microbial inactivation by thermal means. The error splitting method proposed by Theil was used to divide the average squared difference between each observed and predicted datum into three orthogonal error sources: bias, regression, and random error. The method is based on the hypothesis that if the model is accurate, the overall average predicted and observed values should be the same and a plot of observed versus predicted inactivation values should have a slope of 1. The bias fixed error term quantifies the overall average difference between predicted and observed inactivation values. The regression fixed error term quantifies the difference between observed and predicted values near the end of the predictive region, where shoulders and tails may occur. The random error term quantifies the random variability of the predicted versus observed inactivation values. Statistical tests were proposed to determine the significance of each fixed error term and the normality of the random error source. The method was used to discuss the goodness of fit for the three models for Escherichia coli. The best model was the one that minimized total residual error, maximized random error sources (i.e., fixed error terms are not significant), and maximized the coefficient of correlation between observed and predicted inactivation values.