A Beta Asymmetric Unfolding Model for Continuous Bounded Responses

Unfolding models are relevant in all cases when respondents set their agreement levels by searching some optimal level of agreement with an item: They agree to some extent, but not too much. For instance, the more we see the negative consequences of having a baby for a single mother, the more we are likely to find pros about abortion. But the more we would raise our level of agreement in favor of abortion, the more we would be concerned that lives are being stopped, and this would act as a moderator of the first concern. In this situation, responses are shaped by the particular equilibrium each respondent finds between a social concern and a natural concern for life respect. In this talk, we are interested in the general class of situations where an increase in some attitude or behavior A triggers an increase in another attitude or behavior B, that at some point, eventually becomes an inhibitor of the very process that first gave it birth. This mechanism is expressed as an explicit set of differential equations, which, upon integration, leads to a new class of potentially asymmetric unimodal response functions. The obtained solution function is integrated within a Beta Response Model (Noel & Dauvier, 2007; Noel, 2014), which properties are studied, in particular by comparison of previous proposals, and an application on a real dataset is presented and discussed.