TABLE 1.

The four metrics of model evaluation considered in this paper, their formulations, ranges, and descriptions.

Metric	Formula	[Range] (random expectation)	Description
Area under the operator curve (AUC)	$\frac{{\sum }_{i,j}{1}_{p_i>p_j}{y}_i\left(1-y_j\right)}{{\sum }_{i,j}{y}_i\left(1-y_j\right)},$ where the indicator function $1_{p_i>p_j}$ obtains the value of one if $p_i>p_j$, whereas otherwise it obtains the value of zero	[0…1] (0.5)	The proportion of cases for which the occurrence probability for a randomly chosen occupied sampling unit is higher than the occurrence probability for a randomly chosen empty sampling unit. Can be equivalently defined as the integral of the receiver operating characteristic (ROC) curve, plotting sensitivity against 1—specificity over all thresholds (Hanley & McNeil, 1982)
Tjur's R 2	${\overline{p}}_{y=1}-{\overline{p}}_{y=0}$ $=\frac{{\sum }_i{y}_i{p}_i}{{\sum }_i{y}_i}-\frac{{\sum }_i\left(1-y_i\right)p_i}{{\sum }_i\left(1-y_i\right)}$	[−1…1] (0)	The difference in the average occupancy probabilities between occupied and empty sampling units (Tjur, 2009). Can be also interpreted as variance explained by the binary model, hence being to some extent equivalent of the usual R 2 of linear models (Tjur, 2009)
True skill statistic (TSS)	Sensitivity + specificity – 1	[−1…1] (0)	TSS compares the number of correct predictions, minus those attributable to random guessing, to that of a hypothetical set of perfect predictions (Allouche et al., 2006)
Cohen's Kappa	$\frac{A_o-A_e}{1-A_e},$ where $A_o$ and $A_e$ are, respectively, the observed and expected total accuracy	[−1…1] (0)	Overall accuracy of model predictions, corrected by the accuracy expected to occur by chance (Allouche et al., 2006; Shao & Halpin, 1995)