Validation of models with proportional bias

Objective. This paper presents extensions to Freese's statistical method for model-validation when proportional bias (PB) is present in the predictions. The method is illustrated with data from a model that simulates grassland growth. Materials and methods. The extensions to validate models with PB were: the maximum anticipated error for the original proposal, hypothesis testing, and the maximum anticipated error for the alternative proposal, and the confidence interval for a quantile of error distribution. Results. The tested model had PB, which once removed, and with a confidence level of 95%, the magnitude of error does not surpass 1225.564 kg ha-1. Therefore, the validated model can be used to predict grassland growth. However, it would require a fit of its structure based on the presence of PB. Conclusions. The extensions presented to validate models with PB are applied without modification in the model structure. Once PB is corrected, the confidence interval for the quantile 1-α of the error distribution enables a higher bound for the magnitude of the prediction error and it can be used to evaluate the evolution of the model for a system prediction.