The A-not A protocol with sureness produce multinomial observations that are traditionally analyzed with statistical methods for contingency tables or by calculation of an R-index. In this paper it is shown that the Thurstonian model for the A-not A protocol can be written as a cumulative link model including the binormal unequal variances model. The model is extended to allow for explanatory variables and we illustrate how consumer differences can be modeled within the Thurstonian framework on a consumer study of packet soup conducted by Unilever. The extension also allows several test-product variations to be analyzed in the same model providing additional insight and reduced experimental costs. The effects of explanatory variables on the Thurstonian delta, the sensitivity (AUC), the ROC curve and the response category thresholds are discussed in detail. All statistical methods are implemented in the free R-package ordinal (http://www.cran.r-project.org/package=ordinal/).