Subject-specific modelling of paired comparison data: A lasso-type penalty approach

In traditional paired comparison models heterogeneity in the population is simply ignored and it is assumed that all persons or subjects have the same preference structure. In the models considered here the preference of an object over another object is explicitly modelled as depending on subject-specific covariates, therefore allowing for heterogeneity in the population. Since by construction the models contain a large number of parameters we propose to use penalized estimation procedures to obtain estimates of the parameters. The used regularized estimation approach penalizes the differences between the parameters corresponding to single covariates. It enforces variable selection and allows to find clusters of objects with respect to covariates. We consider simple binary but also ordinal paired comparisons models. The method is applied to data from a pre-election study from Germany.