Choice of choice models: Theory of signal detectability outperforms Bradley-Terry-Luce choice model - Kornbrot,Diana E; Georgiou,George J; Page,Mike (PeerJ Preprints, 2018)
Identifying the best framework for two-choice decision-making has been a goal of psychology theory for many decades (Bohil, Szalma, & Hancock, 2015; Macmillan & Creelman, 1991). There are two main candidates: the theory of signal detectability (TSD) (Swets, Tanner Jr, & Birdsall, 1961; Thurstone, 1927) based on a normal distribution/probit function, and the choice-model theory (Link, 1975; Luce, 1959) that uses the logistic distribution/logit function. A probit link function, and hence TSD, was shown to have a better Bayesian Goodness of Fit than the logit function for every one of eighteen diverse psychology data sets (Open-Science-Collaboration, 2015a), conclusions having been obtained using Generalized Linear Mixed Models (Lindstrom & Bates, 1990; Nelder & Wedderburn, 1972) . These findings are important, not only for the psychology of perceptual, cognitive and social decision-making, but for any science that use binary proportions to measure effectiveness, as well as the meta-analysis of such studies.
Keywords: choice models; signat detection; generalized linear mixed models; binary probit; binary logistic; analysis of proprotions