Statistical Modelling in Surveys without Neglecting The Undecided: Multinomial Logistic Regression Models and Imprecise Classification Trees under Ontic Data Imprecision

In surveys, and most notably in election polls, undecided participants frequently constitute subgroups of their own with specific individual characteristics. While traditional survey methods and corresponding statistical models are inherently damned to neglect this valuable information, an ontic random set view provides us with the full power of the whole statistical modelling framework. We elaborate this idea for a multinomial logistic regression model (which can be derived as a discrete choice model for voting behaviour) and an imprecise classification tree, and apply them as a prototypic illustration to the German Longitudinal Election Study 2013. Our results corroborate the importance of a sophisticated, random set-based modelling. Furthermore, by reinterpreting the undecided respondents’ answers as disjunctive random sets, general forecasts based on interval-valued point estimators are calculated.