An approach to combine the logistic threshold model of psychophysics with the Bradley–Terry–Luce models of choice theory

The paper presents a straightforward extension of the Bradley–Terry–Luce model (BTL model) that can be derived from the logistic threshold model of psychophysics which assumes that psychometric functions are logistic probability functions. It is shown that (under weak side conditions) the logistic threshold model is a submodel of the extended BTL model. Moreover, representation and uniqueness theorems are proven that provide some evidence that the extended BTL model is a useful and widely applicable generalization of the ordinary BTL model. Finally, the logistic shape of the psychometric function is derived from axioms about binary choice probabilities. This characterization of the logistic threshold model can replace goodness of fit tests for the logistic probability distribution. r 2004 Elsevier Inc. All rights reserved.