Estimation of the Thurstonian model for the 2-AC protocol

The 2-AC protocol is a 2-AFC protocol with a "no-difference" option and is technically identical to the paired preference test with a "no-preference" option. The Thurstonian model for the 2-AC protocol is parameterized by δ and a decision parameter τ, the estimates of which can be obtained by fairly simple well-known methods. In this paper we describe how standard errors of the parameters can be obtained and how exact power computations can be performed. We also show how the Thurstonian model for the 2-AC protocol is closely related to a statistical model known as a cumulative probit model. This relationship makes it possible to extract estimates and standard errors of δ and τ from general statistical software, and furthermore, it makes it possible to combine standard regression modelling with the Thurstonian model for the 2-AC protocol. A model for replicated 2-AC data is proposed using cumulative link mixed models. Examples will be given throughout the paper and the methodology is implemented in the authors' free R-packages sensR and ordinal.