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Schneider, Micha; Pößnecker, Wolfgang; Tutz, Gerhard (6. August 2019): Variable Selection in Mixture Models with an Uncertainty Component. Department of Statistics: Technical Reports, No.225


Mixture Models as CUB and CUP models provide the opportunity to model discrete human choices as a combination of a preference and an uncertainty structure. In CUB models the preference is represented by shifted binomial random variables and the uncertainty by a discrete uniform distribution. CUP models extend this concept by using ordinal response models as the cumulative model for the preference structure. To reduce model complexity we propose variable selection via group lasso regularization. The approach is developed for CUB and CUP models and compared to a stepwise selection. Both simulated data and survey data are used to investigate the performance of the selection procedures. It is demonstrated that variable selection by regularization yields stable parameter estimates and easy-to-interpret results in both model components and provides a data-driven method for model selection in mixture models with an uncertainty component.