Model evaluation by comparison of model-based predictions and measured values

The appropriateness of a statistical analysis for evaluating a model depends on the model's purpose. A common purpose for models in agricultural research and environmental management is accurate prediction. In this context, correlation and linear regression are frequently used to test or compare models, including tests of intercept a = 0 and slope b = 1, but unfortunately such results are related only obliquely to the specific matter of predictive success. The mean squared deviation (MSD) between model predictions X and measured values Y has been proposed as a directly relevant measure of predictive success, with MSD partitioned into three components to gain further insight into model performance. This paper proposes a different and better partitioning of MSD: squared bias (SB), nonunity, slope (NU), and lack of correlation (LC). These MSD components are distinct and additive, they base straightforward geometric and analysis of variance (ANOVA) interpretations, and they relate transparently to regression parameters. Our MSD components are illustrated using several models for wheat (Triticum aestivum L.) yield. The MSD statistic and its components nicely complement correlation and linear regression in evaluating the predictive accuracy of models.