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Introduction

The Total Operating Characteristic (TOC) is an effective measure to compare a boolean and a rank variable. TOC can be used to measure the ability of an index variable to diagnose either presence or absence of a characteristic. The diagnosis of presence or absence depends on whether the value of an index variable is above a threshold. TOC considers multiple possible thresholds. Each threshold generates a two-by-two Contingency table, which contains four entries: hits, misses, false alarms, and correct rejections.

The Receiver Operating Characteristic (ROC) is commonly used to characterize diagnostic ability although it reveals less information than the TOC. For each threshold, ROC reveals two ratios, hits/(hits + misses) and false alarms/(false alarms + correct rejections), while TOC shows the total information in the contingency table for each threshold. The TOC method reveals all of the information that the ROC method provides, plus additional important information that ROC does not reveal, i.e. the size of every entry in the contingency table for each threshold. The commonly reported Area Under the Curve (AUC) metric is calculable from TOC.

The TOC was first developed by Robert Gilmore Pontius Jr and Kangping Si in 2013 for application in land change science. TOC can also be used to analyze spatial and non-spatial data and measure diagnostic ability in fields including but not limited to: medical imaging, weather forecasting, remote sensing, and materials testing. For a video introduction to the TOC and its utility in land change modeling, please click here.

Basic Concept