A Social Desirability Item Response Theory Model: Retrieve-Deceive-Transfer

In this study, a new item response theory model is developed to account for situations in which respondents overreport or underreport their actual opinions on a positive or negative issue. Such behavior is supposed to be a result of deception and transfer mechanisms. In the proposed model, this behavior is simulated by incorporating a deception term into a multidimensional rating scale model, followed by multiplication by a transfer term, with the two operations performed by an indicator function and a transition matrix separately. The proposed model is presented in a Bayesian framework approximated by Markov chain Monte Carlo algorithms. Through a series of simulations, the parameters of the proposed model are recovered accurately. The methodology is also implemented within an online experimental study to demonstrate the methodology's application.