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Generalized linear models are a general class of regressionlike models for continuous 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 in terms of a shift in the location of an underlying 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 application of statistical decision theory to engineering problems, in particular, the detection of a signal embedded in noise. The relevance of the theory to psychophysical studies of detection, recognition, and discrimination was recognized early on by Tanner and Swets (1954) and others (see Green & Swets, 1966). SDT has in recent years been applied to a wide variety of research in psychology (

An extension of signal detection theory (SDT) that incorporates mixtures of the underlying distributions is presented. The mixtures can be motivated by the idea that a presentation of a signal shifts the location of an underlying distribution only if the observer is attending to the signal; otherwise, the distribution is not shifted or is only partially shifted. Thus, trials with a signal presentation consist of a mixture of 2 (or more) latent classes of trials. Mixture SDT provides a general theoretical framework that offers a new perspective on a number of findings. For example, mixture SDT offers an alternative to the unequal variance signal detection model; it can also account for nonlinear normal receiver operating characteristic curves, as found in recent research.Signal detection theory (SDT) provides a theoretical framework that has been quite useful in psychology and other fields (see Gescheider, 1997;Macmillan & Creelman, 1991;Swets, 1996). A basic idea of SDT is that decisions about the presence or absence of an event are based on decision criteria and on perceptions of the event or nonevent, with the perceptions being represented by probability distributions on an underlying continuum. Thus, in its simplest form, the theory considers two basic aspects of detection-the underlying representations, which are interpreted as psychological distributions of some sort (e.g., of perception or familiarity), and a decision aspect, which involves the use of decision criteria to arrive at a response.The present article extends SDT by viewing detection as consisting of an additional process. The result is a simple and psychologically meaningful extension of SDT that can be applied to any area of research where SDT has been applied. The approach is illustrated with applications to research on recognition memory, where the additional process can be interpreted as attention. In particular, the basic idea is that presentation of a signal shifts the location of the underlying distribution only if the observer is attending to the signal; otherwise, the distribution is not shifted or is only partially shifted. As a result, trials with a signal presentation consist of a mixture of two (or more) latent classes of trials, which can be interpreted as being attended and nonattended trials (or as two different levels of processing of the stimuli). Apart from that, the theory is the same as in conventional SDT, in that the underlying representations are used together with response criteria to arrive at an observed response. I show, however, that this simple extension of SDT is quite powerful and can account for a variety of findings across several areas of research. For example, the mixture approach offers an alternative to the unequal variance signal detection model (Green & Swets, 1966), which has been the standard model for many years, and provides a different interpretation of normal receiver operating characteristic (ROC) curves with slopes less than unity; it can also account for nonlinear normal ROC curves, as found in r...

Research on sequential effects in magnitude scaling is reviewed, and its implications about the adequacy of current time series regression models is discussed. A regression model that unifies what at first appear to be contradictory results is proposed. Theoretical models of judgment and perception are introduced, and their relation to alternative regression models is clarified. A theoretical model of relative judgment that clarifies the role of judgmental error and frames of reference in magnitude scaling is examined in detail. Four experiments that test the model are presented. The results, along with recent results presented by Ward (1987), provide support for the model. The importance of being explicit about the relation of theoretical models to regression models and about the role of error in these models is discussed.

Source memory has become the focus of a growing number of investigations in a variety of fields. An appropriate model for source memory is, therefore, of increasing importance. A simple 2-dimensional signal-detection model of source recognition is presented. The receiver operating characteristics (ROCs) obtained from 3 experiments are then used to test the model. The data demonstrate 3 regularities: convex ROCs, z-ROCs with linear slopes of 1.00, and slightly concave z-ROCs. Two of these regularities support the model. The 3rd requires a revision of the model. This revised model is fitted to the data. The implications of these regularities for other theories are also discussed.