Ecological fallacy and covariates in the estimation of voters transitions

TL;DR

This paper analyzes the conditions under which ecological bias occurs in voter transition estimation and shows that incorporating covariates into models can sometimes mitigate or fail to correct this bias, especially with weak associations.

Contribution

It provides a formal framework for understanding ecological bias and demonstrates when covariate-based models can or cannot correct for it in ecological inference.

Findings

Ecological bias occurs under specific conditions related to covariate effects.

Incorporating covariates can sometimes correct bias, but not always.

Weak associations and similar transition probabilities hinder bias correction.

Abstract

We provide a simple formulation of the conditions under which ecological bias should be expected and argue that the bias will affect any method of ecological inference; our claim is supported by formal derivations and several examples where individual data are available. The conditions which we highlight imply that, when they are violated, ecological bias cannot be avoided unless the a suitable model for the effect of specific covariates is incorporated into ecological inference. We also detect situations where the ecological bias cannot be corrected even if the effect of covariates is incorporated into the model. In particular, when the association in the individual data is rather weak and certain transition probabilities are similar functions of a given covariate, ecological inference methods may be unable to disentangle the individual components from their aggregate. In any case, the value of the covariates measured at the level of local units, when these are rather extensive, do not provide enough information on the within unit heterogeneity. Our findings are applied and tested on several data sets, both real and simulated, where individual observations are available in addition to the aggregated ones.,.