Optimal choice of electoral preference data

Electoral researchers are so much accustomed to analyzing the choice of the single most preferred party as the left-hand side variable of their models of electoral behavior that they often ignore revealed preference data. Drawing on random utility theory, their models predict electoral behavior at the extensive margin of choice. Since the seminal work of Luce and others on individual choice behavior, however, many social science disciplines (consumer research, labor market research, travel demand, etc.) have extended their inventory of observed preference data with, for instance, multiple paired comparisons, complete or incomplete rankings, and multiple ratings. Eliciting (voter) preferences using these procedures and applying appropriate choice models is known to considerably increase the efficiency of estimates of causal factors in models of (electoral) behavior. In this paper, we demonstrate the efficiency gain when adding additional preference information to first preferences, up to full ranking data. We do so for multi-party systems of different sizes. We use simulation studies as well as empirical data from the 1972 German election study. Comparing the practical considerations for using ranking and single preference data results in suggestions for choice of measurement instruments in different multi-candidate and multi-party settings.

Use of posterior predictive assessments to evaluate model fit in multilevel logistic regression

Assessing the fit of a model is an important final step in any statistical analysis, but this is not straightforward when complex discrete response models are used. Cross validation and posterior predictions have been suggested as methods to aid model criticism. In this paper a comparison is made between four methods of model predictive assessment in the context of a three level logistic regression model for clinical mastitis in dairy cattle; cross validation, a prediction using the full posterior predictive distribution and two “mixed” predictive methods that incorporate higher level random effects simulated from the underlying model distribution. Cross validation is considered a gold standard method but is computationally intensive and thus a comparison is made between posterior predictive assessments and cross validation. The analyses revealed that mixed prediction methods produced results close to cross validation whilst the full posterior predictive assessment gave predictions that were over-optimistic (closer to the observed disease rates) compared with cross validation. A mixed prediction method that simulated random effects from both higher levels was best at identifying the outlying level two (farm-year) units of interest. It is concluded that this mixed prediction method, simulating random effects from both higher levels, is straightforward and may be of value in model criticism of multilevel logistic regression, a technique commonly used for animal health data with a hierarchical structure.