Distances in Latent Space: A Novel Approach to Analyzing Conjoints

Simon Hoellerbauer (University of North Carolina, Chapel Hill)

Abstract:  Recent work (Abramson, Kocak, and Magazinnik, n.d.) has shown the potential pitfalls of using conjoint analysis to understand aggregate preferences over alternative profiles. Adapting recent work that frames conjoint analysis in an IRT framework (Caughey, Katsumata, and Yamamoto, n.d.), I propose conceiving of conjoint profiles as defining a location in a latent space, relative to which individuals position themselves. In a traditional forced-choice conjoint, individuals will choose the alternative whose location lies closer to their ideal point. Leveraging a parametric assumption about each alternative's location as a function of its profile, I estimate the distance between an individual's ideal point and the profile location. I then construct distance estimates for profiles that are not involved in the estimation process and ask respondents other questions about these additional profiles. Specifically, I am interested in estimating individuals' affinity for an organization and how affinity influences how likely individuals are to engage with an organization. I therefore ask respondents to pick the profile from a pair with which they identify more strongly, and then separately ask about engagement with the organizations in the pair. The design proposed here allows me to capture how organization attributes influence affinity while also seeing how that affinity itself impacts individual engagement with organizations. Applying a traditional conjoint analysis to both questions would assume that attributes influence both outcomes in similar ways and conflates affinity and willingness to engage with an organization. I combine all analysis in a fully Bayesian model that estimates ideal points, profile location parameters, and the effect of the distance between the two on outcomes of interest. In this paper, I describe the statistical model I propose, demonstrate its properties via a simulation study, and also employ it on new data from a survey on organizational engagement among college students.

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