A latent choice model to analyze the role of preliminary preferences in shaping observed choices

When selecting among a set of alternatives, individuals often compare each alternative with reference to some preliminary preference (PP). The preliminary preference could be the individual's preferred global option (i.e., their ideal choice) or the most ideal option within the current choice set. Previous research has shown that loss of an attribute relative to that of the PP has a stronger impact on the individual's choice compared to gain of that attribute—a phenomenon commonly known as loss aversion. To incorporate this loss aversion into choice modeling, the PP of the individuals must then be known; however, such information is generally not available when observing individual's choice behavior. To overcome the lack of knowledge of an individual's PP, this study proposes a probabilistic approach where all alternatives in the choice set have some potential of being an individual's PP. A multinomial logit (MNL) based methodology, named the latent preliminary preference (LPP) model, is used to estimate the PP probabilities entirely as a function of the decision-maker characteristics and each alternative's attributes, which overcomes the complexity that arises when choices are unlabeled. In addition, the methodology accommodates inertia that some individual's may have toward their PP, as well as the desire to try new options. Moreover, this study proposes randomizing the parameters of LPP model to account for random taste heterogeneity of individuals that would arise in a panel dataset, giving rise to random parameter latent preliminary preference (RPLPP) model. The ability of maximum likelihood inference method to retrieve the parameters of fixed parameters LPP model is demonstrated on synthetic data. The statistical significance and bias in estimated parameters are also demonstrated. The proposed model is then applied on a parking preference survey to examine the presence of loss aversion and inertia/variety seeking behavior among the respondents.