Modeling electoral choices in multiparty systems with high-dimensional data: A regularized selection of parameters using the lasso approach

Abstract

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.

High-Dimensional LASSO-Based Computational Regression Models: Regularization, Shrinkage, and Selection

“…For studying diseases it has been used for investigating infection diseases [36], various cancer types [37,38], diabetes [39], and cardiovascular diseases [40]. In the computational social sciences the LASSO has been used to study data from social media [41], the stock market [42], economy [43], and political science [44]. Further application areas include robotics [45], climatology [46], and pharmacology [47].…”

Selective inference for effect modification via the lasso

“…Our method can also be used in non-causal regression problems when the interest is on the interaction terms between some low-dimensional primary variables (not necessarily a treatment) and some high-dimensional covariates. Examples include gene-environment interaction (Crossa et al, 2010, Biswas et al, 2014, interaction between species traits and environment in ecology (Brown et al, 2014), and subgroup-specific reactions to political issues when modeling electoral choices (Mauerer et al, 2015). In these examples, the applied researchers often want to make statistical inference for a selected interaction model.…”

BTLLasso: A Common Framework and Software Package for the Inclusion and Selection of Covariates in Bradley-Terry Models

“…Spatial election theory then explains the party choice of voters by a utility function that depends on the distance between the voter's own position and that of the parties within the space of policy-dimensions. For details see, for example, Thurner and Eymann (2000) and Mauerer, Pössnecker, Thurner, and Tutz (2015). In the election data, the covariates SocEc, Immigration and Climate measure the distance between participants and the single parties on three different political dimensions and are, therefore, considered as subject-object-specific covariates.…”