2.5 Model Evaluation
The coefficient of determination (R2) in validation
dataset, root mean square error of prediction (RMSEP) and ratio of
performance deviation (RPD) were used to evaluate models. Ranking was
made on the basis of RPD values; higher the RPD better was the model
performance. When two models had same RPD values, R2values were referred to, and models with higher R2value better explained the fitted data. When two models had same RPD and
R2 values, the RMSE values were referred to, and
models with lower RMSE gave better prediction/ validation of data than
those with higher RMSE. The R2, PMSE
and RPD were calculated as:
\(R^{2}=1-\left(\frac{{\sum_{i}{n\left(Y_{\text{Pred}}-Y_{\text{measured}}\right)}}^{2}}{{\sum_{i}n\ Y_{i}-Y_{\text{mean}}\ }^{2}}\right)\)……… (3)
\(RMSE=\sqrt{\frac{{\sum_{i}{n\left(Y_{\text{Pred}}-Y_{\text{measured}}\right)}}^{2}}{n-1}}\)………. (4)
\(RPD=\frac{\text{SD}_{\text{val.}}}{\text{RMSE}}\)………….. (5)
Where, Ypred = predicted values; Ymean = mean of measured values; Y meas
= measured values; n= number of predicted or measured values with I =
1,2,…n; SDval= standard deviation of measured values in the
validation dataset; and RMSEP = root mean square error of prediction in
validation dataset. The procedure used for model calibration and
validation is presented: