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Abstract: The relative operating characteristic (ROC) and the Total operating characteristic (TOC) are the most popular statistical method to compare a variable that shows Presence or Absence versus a ranked variable. The interpretation of their curves, along with their Area Under the Curve (AUC), is used as a measure of the strength of the monotonic relationship between the two variables. All these metrics give equal weight to all the values along the curves, which leads to equal evaluation of less relevant regions of the graph as prevalence gets lower. We propose the use of both the Figure of Merit (FOM) and its area (AFOM) for applications where the initial values of the rank variable are more relevant. We show how FOM concentrates more area around prevalence, making it a more representative measure for cases with lower prevalence. We illustrate the concepts with an application to land change science.

Julen Perales is a PhD student in Economics at Public University of Navarra. His research focuses on Land Use Change modeling. He is currently working on model validation, a research field which he has developed though a research stay at Clark University, MA. He is also working on categorical spatiotemporal time series analysis.