The increased usage of discrete choice models in the analysis of multiparty elections faces one severe challenge: the proliferation of parameters, resulting in high-dimensional and difficult-to-interpret models. For example, the application of a multinomial logit model in a party system with J parties results in maximally J−1 parameters for chooser-specific attributes (e.g., sex and age). For the specification of alternative-specific attributes (usually: positions on issues and issue distances), maximally J parameters for each political issue can be estimated. Thus, a model of party choice with five parties based on three political issues and ten voter attributes already produces 59 possible coefficients. As soon as we allow for interaction effects to detect segment-specific reactions to issues, the situation is even aggravated. In order to systematically and efficiently identify relevant predictors in voting models, we derive and use Lasso-type regularized parameter selection techniques that take into account both individual- and alternative-specific variables. Most importantly, our new algorithm can handle for the first time the alternative-wise specification of the attributes of alternatives. Applying the specifically adjusted Lasso method to the 2009 German Parliamentary Election, we demonstrate that our approach massively reduces the models' complexity and simplifies their interpretation. Lasso-penalization clearly outperforms the simple ML estimator. The results are illustrated by innovative visualization methods, the so-called effect star plots.
