Covariates in the eforensics Model
Walter R. Mebane, Jr.

Election forensics is the use of statistical methods to determine whether the results of an election accurately reflect the intentions of the electors.  The eforensics model is a finite mixture measurement model that uses Bayesian methods to produce valid (but imperfect) aggregation unit estimates of the incidence and magnitude of realized election frauds, using as input aggregation unit (e.g., polling station) counts of eligible voters and of votes cast for the ballot alternatives.  I discuss how observed covariates are used in eforensics.  Covariates allow data from elections for different offices to be pooled, for example the elections for different seats in a single-member district legislative election, but more generally covariates can be thought of as reducing reliance on the independent and mostly Normal priors for unknown parameters that eforensics uses.  Ecological correlation concerns prevent deploying covariates that naively may appear to be meaningful, but geographically defined fixed effects are nonetheless generally useful.  Geographic fixed effects often improve the performance of the model in terms of reducing or eliminating mixture probability MCMC posterior multimodality.  Geographic fixed effects are often helpful when used not only in the model's turnout and vote choice equations but also when used to condition the magnitudes of eforensics-frauds.  These work, I speculate, by allowing the frauds-related aspects of the model to engage more cleanly with the higher-order dependencies election frauds induce among aggregation unit observed counts.