Generalized linear and additive models for psychophysical data

Abstract

What do such diverse paradigms as classification images, difference scaling and additive conjoint measurement have in common? We introduce a general framework that permits modeling and evaluating experiments covering a broad range of psychophysical tasks. Psychophysical data are considered within a signal detection model in which a decision variable, d, which is some function, f, of the stimulus conditions, S, is related to the expected probability of response, E[P], through a psychometric function, G: E[P] = G(f(d(S))). In many cases, the function f is linear, in which case the model reduces to E[P] = G(Xb), where X is a design matrix describing the stimulus configuration and b a vector of weights indicating how the observer combines stimulus information in the decision variable. By inverting the psychometric function, we obtain a Generalized Linear Model (GLM). We demonstrate how this model, which has previously been applied to calculation of signal detection theory parameters and fitting the psychometric function, is extended to provide maximum likelihood solutions for three tasks: classification image estimation, difference scaling and additive conjoint measurement. Within the GLM framework, nested hypotheses are easily set-up in a manner resembling classical analysis of variance. In addition, the GLM is easily extended to fitting and evaluating more flexible (nonparametric) models involving arbitrary smooth functions of the stimulus. In particular, this approach permits a principled approach to fitting smooth classification images.