Social influence cannot be identified from purely observational data on social networks, because such influence is generically confounded with latent homophily, i.e., with a node's network partners being informative about the node's attributes and therefore its behavior. If the network grows according to either a latent community (stochastic block) model, or a continuous latent space model, then latent homophilous attributes can be consistently estimated from the global pattern of social ties. We show that, for common versions of those two network models, these estimates are so informative that controlling for estimated attributes allows for asymptotically unbiased and consistent estimation of social-influence effects in linear models. In particular, the bias shrinks at a rate which directly reflects how much information the network provides about the latent attributes. These are the first results on the consistent non-experimental estimation of social-influence effects in the presence of latent homophily, and we discuss the prospects for generalizing them.
翻译:社会网络的纯观察数据无法确定社会影响,因为这种影响一般都与潜在的同质性混为一谈,即一个节点的网络伙伴对节点的属性及其行为具有了解性。如果网络按照潜在的社区(随机区块)模型或连续的潜在空间模型增长,那么从全球社会联系模式中可以持续地估计潜在的同质性属性。我们表明,对于这两个网络模型的共同版本来说,这些估计非常丰富,因此,对估计特性的控制可以允许对线性模型的社会影响进行无差别和一致的估计。特别是,偏见缩小的速度直接反映了网络提供的关于潜在属性的信息量。这是在潜在同质存在的情况下对社会影响持续进行非探索性估计的第一个结果,我们讨论了将其普遍化的前景。