生态谬误和协变量：基于个体数据多层次建模的新见解
Ecological fallacy and covariates: new insights based on multilevel modelling of individual data
摘要：
本文讨论了生态推理中的生态偏差问题。我们提供了一个明确的制定所需的条件，为普通的生态回归产生无偏估计，并认为，当这些条件被违反，任何方法的生态推断将产生有偏估计。这些研究结果的澄清和支持的经验证据提供的三个主要的生态推理方法与适用于一组独特的个人数据的投票行为的多层次逻辑斯谛回归的结果进行比较。我们的研究的主要发现有两个重要的影响，适用于所有的情况下，没有生态偏见的条件被违反：（i）只有生态推理方法，允许模型的影响协变量有机会产生无偏估计;（ii）一套协变量被包括在模型中，以消除偏见是有限的边际比例。最后，我们的研究结果表明，当两个生态变量之间的关联是非常弱的，它是不可能获得无偏估计，即使是一个适当的模型，占相关协变量的影响。
英文摘要：
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.
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