Threshold Models and Choice Theory
Detection theory models have faced three classes of competitors. First, before the advent of detection theory, much of psychophysics was concerned with measuring “thresholds, ” below which stimuli were thought not to be perceived. Second, in the 1950s and early 1960s, as Tanner, Green, and Swets were developing signal detection theory, Luce (1959, 1963a) proposed Choice Theory, a conceptually different analysis of a similar range of experiments. Third, one reaction to detection theory has been an attempt to avoid the “parametric” assumption that the underlying distributions are Gaussian.
These three lines of work occupy distinct psychophysical niches in the current research environment. Choice Theory differs only slightly from detection theory in the simplest cases, but its quite different framework allows for a wide range of application. Threshold concepts lead to models that describe most data less well than detection theory; there are exceptions, however, and threshold ideas have been extended usefully to “multinomial” models of complex tasks. “Nonparametric” measures have turned out, on examination, to be related to threshold theory, Choice Theory, or both, and they are just as theory-bound as other statistics. We discuss explicit threshold models first, then Choice Theory, and then “nonparametric” analysis.
Threshold theory (Krantz, 1969; Luce, 1963a) assumes that the decision space is characterized by a few discrete states, rather than the continuous dimensions of detection theory. Different threshold models propose different connections between stimulus classes and discrete internal states, and between internal states and responses. For most models, we develop a state diagram that spells out these connections and defines the model. From the state diagram, the form of the implied ROC can be deduced; for those mod-