Analyzing faking-good response data: Combination of a Replacement and a Binomial(CRB) distribution approach

In this short paper, we describe a novel approach to model and analyse ordinal data in the presence of faking behavior, namely the tendency of the survey’s participants to falsify their responses in order to achieve a particular purpose. The proposal relies on the use of two statistical approaches commonly used to analyse faking and preference data: the Sampling Generation by Replacement (SGR) and Combination of Uniform and Binomial distributions (CUBE). By combining both SGR and CUBE, we propose CRB (Combination of Replacement and Binomial distributions), where the response ordinal measure is modeled as a convex combination of the shifted-Binomial distribution and the Replacement distribution. Thus, the first component aims to represent the response measure unaffected by faking behavior whereas the second element of the linear model represents the result of a faking strategy. As for the CUBE models, CRB parameters are estimated via Maximum likelihood by means of the EM algorithm. Finally, an application to ordinal data is proposed to show how the CRB model can be used to analyse self-reported data potentially affected by faking behavior.