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

This paper deals with the issue of ecological bias in ecological inference. We provide an explicit formulation of the conditions required for the ordinary ecological regression to produce unbiased estimates and argue that, when these conditions are violated, any method of ecological inference is going to produce biased estimates. These findings are clarified and supported by empirical evidence provided by comparing the results of three main ecological inference methods with those of multilevel logistic regression applied to a unique set of individual data on voting behaviour. The main findings of our study have two important implications that apply to all situations where the conditions for no ecological bias are violated: (i) only ecological inference methods that allow to model the effect of covariates have a chance to produce unbiased estimates; (ii) the set of covariates to be included in the model to remove bias is limited to the marginal proportions. Finally, our results suggest that, when the association between two ecological variables is very weak, it is not possible to obtain unbiased estimates even by an appropriate model that accounts for the effect of relevant covariates.