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This paper deals with the issue of ecological bias in ecological inference.We provide an explicit formulation of the conditions required for the ordinaryecological regression to produce unbiased estimates and argue that, when theseconditions are violated, any method of ecological inference is going to producebiased estimates. These findings are clarified and supported by empiricalevidence provided by comparing the results of three main ecological inferencemethods with those of multilevel logistic regression applied to a unique set ofindividual data on voting behaviour. The main findings of our study have twoimportant implications that apply to all situations where the conditions for noecological bias are violated: (i) only ecological inference methods that allowto 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 islimited to the marginal proportions. Finally, our results suggest that, whenthe association between two ecological variables is very weak, it is notpossible to obtain unbiased estimates even by an appropriate model thataccounts for the effect of relevant covariates.

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