Signal detection theory and generalized linear models.

Abstract

Generalized linear models are a general class of regressionlike models for continu-ous and categorical response variables. Signal detection models can be formulated as a subclass of generalized linear models, and the result is a rich class of signal detection models based on different underlying distributions. An example is a signal detection model based on the extreme value distribution. The extreme value model is shown to yield unit slope receiver operating characteristic (ROC) curves for several classic data sets that are commonly given as examples of normal or logistic ROC curves with slopes that differ from unity. The result is an additive model with a simple interpretation i terms of a shift in the location of an under-lying distribution. The models can also be extended in several ways, such as to recognize response dependencies, to include random coefficients, or to allow for more general underlying probability distributions. Signal detection theory (SDT) arose as an applica-tion of statistical decision theory to engineering prob-lems, in particular, the detection of a signal embedded in noise. The relevance of the theory to psychophysi-cal studies of detection, recognition, and discrimina-tion was recognized early on by Tanner and Swets