Mauerer, Ingrid; Pößnecker, Wolfgang; Thurner, Paul W.; Tutz, Gerhard
(9. April 2014):
Modeling electoral choices in multiparty systems with high-dimensional data: A regularized selection of parameters using the Lasso approach.
Department of Statistics: Technical Reports, No.158
The increasing popularity of the Spatial Theory of Voting has given rise to the frequent usage of multinomial logit or probit models with alternative-specific covariates. The flexibility of these models comes along with one severe drawback: the proliferation of coefficients, resulting in high-dimensional and difficult-to-interpret models. In particular, choice models in a party system with J parties result in maximally J-1 parameters for each chooser-specific attribute (e.g., sex, age). For the specification of alternative-specific attributes (e.g., issue distances), maximally J parameters per attribute can be estimated. As soon as we allow for interaction effects, e.g., to test for segment-specific reactions to issue distances, the situation is even aggravated. In order to systematically identify relevant predictors in spatial voting models with non-policy factors, we derive and use for the first time Lasso-type regularized parameter selection techniques that take into account both the categorical structure of the response variable (i.e., party choice) and the alternative-wise specification of alternative-specific attributes. By applying the Lasso method to the 2009 German Parliamentary Election, we demonstrate that our approach massively reduces the model's complexity, simplifies its interpretation and improves the model's predictive performance. Lasso-penalization clearly outperforms the simple ML estimator. The results are illustrated by innovative visualization methods, so-called effect star-plots.