In Appendix A we provide the tabled results of the (Nested) Conditional Logit Models 1 presenting all variables and parameter estimates. These models are the basis for all calculations and visual presentations in the paper. In Appendix B we offer three robustness-checks of the main results in the paper. Robustness-Check I shows that the paper's main conclusions persist when applying quadratic utility losses instead of the used simple linear utility losses. In addition, it provides empirical evidence in favour of the simple linear loss function (Section B.1). Robustness-Check II demonstrates that the main results hold when omitting party identification (PI) and candidate evaluations and considering instead socio-demographic controls and the Left-Right meta issue (Section B.2). For both Robustness-Checks we first provide a summary comparing the identified party-specific issue effects based on these alternative specifications.Second, we offer a comparison of the corresponding linear regression models testing our hypotheses.Third, each Robustness-Check closes with a tabled presentation of the (Nested) Conditional Logit Models based on differing model specifications and control variables, respectively. Finally, Robustness-Check III provides information on the robustness of the paper's findings on the occurrence of party-specific issue voting by excluding the party-specific issue effects with regard to the Greens (Section B.3).

The increasing popularity of the Spatial Theory of Voting has given rise to the frequent usage of multinomial logit/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 chooser-specific attributes (e.g., sex, age). For the specification of alternative-specific attributes (e.g., issue distances), maximally J parameters can be estimated. Thus, a model of party choice with five parties based on three 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 identify relevant predictors in spatial voting models, we derive and use for the first time Lasso-type regularized parameter selection techniques that take into account both individualand alternative-specific variables. Most importantly, our new algorithm can handle the alternative-wise specification of issue distances. Applying the Lasso method to the 2009 German Parliamentary Election, we demonstrate that our approach massively reduces the model's complexity and simplifies its interpretation. Lassopenalization clearly outperforms the simple ML estimator.

Empirical applications of the spatial theory of elections typically rely on the discrete choice framework to arrive at probabilistic voting models. Whereas in the classic model voter choice is solely a function of spatial proximity, neo-Downsian models also incorporate voter-specific nonpolicy attributes, which are represented by sociodemographic characteristics. One prominent line of such probabilistic models, Schofield’s Valence Model, additionally includes party valences into voter utility functions. The model rests on the estimated party intercepts to measure the valence advantages empirically. The party intercepts are ordered based on their values, and then this valence ranking is used further to predict equilibrium locations. The paper demonstrates that this measurement strategy does not provide unique results in fully specified models due to central properties of discrete choice models and the specific nature of party intercepts in these models. Drawing on a simple example based on mass election surveys from Germany, it is shown that the valence ranking, the crucial factor to investigate how valence differences affect the nature of spatial competition, is highly sensitive to arbitrary coding decisions. As a consequence, it is impossible to represent valence with the constants and to infer something substantial from the resulting valence ranking.

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