Ecological fallacy and covariates: new insights based on multilevel modelling of individual data

The paper provides a new and more explicit formulation of the assumptions needed by the ordinary ecological regression to provide unbiased estimates and clarifies why violations of these assumptions will affect any method of ecological inference. Empir- ical evidence is provided by showing that estimates provided by three main ecological inference methods are heavily biased when compared to multilevel logistic regression applied to a unique set of individual data on voting behaviour. The main findings of our paper have two important implications that apply to all situations where the assumptions needed to apply ecological inference are violated in the data; (i) only ecological inference methods that allow one to model the effect of covariates have a chance to produce unbiased estimates, (ii) there are certain data generating mechanisms producing a kind of bias in ecological estimates which cannot be corrected by modelling the effect of covariates.