Estimating the parameters of a model of visual search from ROC data: an alternate method for fitting proper ROC curves

The binormal receiver operating characteristic (ROC) model often predicts an unphysical "hook" near the upper-right corner (1,1) of the ROC plot. Several models for fitting proper ROC curves avoid this problem. The purpose of this work is to describe another method that involves a model of visual search that models free-response data, and to compare the search-model predicted ROC curves with those predicted by PROPROC (proper ROC) software. The highest rating rule was used to infer ROC data from FROC data. An expression for the search-model ROC likelihood function is derived, maximizing which yielded estimates of the parameters and the fitted ROC curve. The method was applied to a dual-modality 5-reader FROC data set. The relative difference between the average AUCs for the two methods was less than 1%. A linear regression of the AUCs yielded an adjusted R-squared of 0.95 indicative of strong linear correlation between the search model AUC and PROPROC AUC, although the shapes of the predicted ROC curves were qualitatively different. This study shows the feasibility of estimating parameters characterizing visual search from data acquired in a non-search paradigm.