Ignoramus, Ignorabimus? On Uncertainty in Ecological Inference

Abstract

Models of ecological inference (EI) have to rely on crucial assumptions about the individuallevel data-generating process, which cannot be tested because of the unavailability of these data. However, these assumptions may be violated by the unknown data and this may lead to serious bias of estimates and predictions. The amount of bias, however, cannot be assessed without information that is unavailable in typical applications of EI. We therefore construct a model that at least approximately accounts for the additional, nonsampling error that may result from possible bias incurred by an EI procedure, a model that builds on the Principle of Maximum Entropy. By means of a systematic simulation experiment, we examine the performance of prediction intervals based on this second-stage Maximum Entropy model. The results of this simulation study suggest that these prediction intervals are at least approximately correct if all possible configurations of the unknown data are taken into account. Finally, we apply our method to a real-world example, where we actually know the true values and are able to assess the performance of our method: the prediction of district-level percentages of split-ticket voting in the 1996 General Election of New Zealand. It turns out that in 95.5% of the New Zealand voting districts, the actual percentage of splitticket votes lies inside the 95% prediction intervals constructed by our method.

Estimation of voter transitions based on ecological inference: an empirical assessment of different approaches

“…Furthermore, ecological inference suffers from crucial methodological problems and is notoriously plagued by an indeterminacy problem (Elff et al 2008;Cho and Manski 2008). In mathematical statistics it is characterized as an ill posed problem, while econometricians consider it as problem with unidentified parameters.…”

An evaluation of the performance and suitability of R × C methods for ecological inference with known true values

“… 4 Several other methods have been proposed for the estimation of R × C tables [see for instance King et al ( 2004 ), Park et al ( 2014 ), Elff et al ( 2008 ), Forcina et al ( 2012 ), Colombi and Forcina ( 2016 )]. Our exclusive focus on the Goodman ( 1953 ), Rosen et al ( 2001 ) and the Greiner and Quinn ( 2009 ) methods is due to several reasons.…”

Combining Aggregate Data and Exit Polls for the Estimation of Voter Transitions

“…While this also improves the coverage rate of the credibility intervals, the observed coverage rate of these credibility intervals is still too low as compared to common standards. Note that a discussion of the appropriate calculation of confidence/credibility intervals is nearly inexistent in the ecological inference literature (one exception is, e.g., Elff, Gschwend, and Johnston 2008) and a calculation is even not possible for every modeling approach there. Also, the coverage rate of credibility/confidence intervals for estimations based on biased individual-level data depends strongly on the validity of the applied assumption.…”