Previous studies have provided comparable information for model evaluation indices (for some models or in general). However, there is no full standardization (or concrete proposals), including newly developed indices. The objective of this study is to verify and evaluate the available indices for model performance evaluation and to examine a logical, interpretable and unique index for general use in model evaluation. R, R2 and RMSE have been considered non-logical, ambiguous and misinterpreted by previous studies (and have been widely suggested from the range of performance indicators) as well as in this study. Quantifying the proximity of two data sets is a common and necessary undertaking in the field of scientific research. The pearson-moment r correlation coefficient is a widespread measure of the degree of linear dependence between two sets of data, but gives no indication of the similarity of the values of these series in size. Although a number of indices have been proposed to compare a dataset to a reference, little data is available to compare two datasets with equivalent (or unknown) reliability. After a brief review and numerical testing of the metrics designed to accomplish this task, this document shows how an index proposed by Mielke can, with a minor modification, satisfy a number of desired characteristics, namely a dimensional, limited, symmetrical, easy to calculate and directly interpretable in relation to r. We therefore show that this index can be considered a natural extension to r, which regulates the downward r value according to the distortion between the data sets analyzed.
The document also proposes an effective way to unravel the systematic and non-systematic contribution to this agreement on the basis of own decompositions. The use and value of the index are also illustrated on synthetic and real data sets. Smaller ME values in absolute terms indicate a better match between the measured values and the calculated values. Positive values indicate positively distorted calculated values (predictions), while negative values show negatively distorted calculated values (sub-predictions). In this case, the baseline of the μ denominator is defined on the basis of both and. However, this last index presents a number of serious defects that are illustrated in the analysis below. The denominator in the equation above is called potential error. AI is a non-dimensional and limited measurement with values closer to 1, indicating better match. The four terms of the denominator can be represented geometrically, as stated in the Supplementary Information section. Following the explicit addition of the term covariance, the index ensures that if X and Y are negatively correlated, an index is zero if it can be seen in Figure 3.
However, if the denominator is unnecessarily inflated by this term of covariance, the counter will be smaller and smaller due to the negative sign in front of the covarianzterm in the equation (10).