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Death to ROC: Birth of the Total Operating Characteristic (TOC)

Authors: Robert Pontius*, Clark University
Topics: Spatial Analysis & Modeling, Geographic Information Science and Systems, Remote Sensing
Keywords: ROC, TOC, GIS, measurement, metric, map comparison, land change
Session Type: Paper
Presentation File: No File Uploaded


The Relative Operating Characteristic (ROC) is a popular method to compare a Rank variable that shows relative priority with a Binary variable that shows presence versus absence. Applications abound in many fields, including in GIS and Remote Sensing where there is frequently a need to compare a map of the probability of a category with a map of the actual category. ROC is almost brilliant in how ROC synthesizes results across various thresholds of the Rank variable. Each threshold produces a table that contains four entries: Hits, Misses, False Alarms, and Correct Rejections. However, ROC fails to reveal any of the entries because the ROC presents results in terms of two ratios at each threshold. The Total Operating Characteristic (TOC) follows an algorithm similar to ROC’s algorithm to examine various thresholds of the Rank variable. However, the TOC succeeds in revealing at each threshold the sizes of Hits, Misses, False Alarms and Correct Rejections. The TOC shows immediately additional important information, specifically the size of the extent and the abundance of presence in the Binary variable, which the ROC fails to show. The TOC gives strictly more information that the ROC, while the TOC allows all of the helpful interpretation of the ROC, such as the shape of the curve and the area under the curve. Users can compute the TOC by using the TOC package in the free software R. Researchers should abandon the ROC and instead adopt the TOC.

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