Why and When "Flawed" Social Network Analyses Still Yield Valid Tests of no Contagion

Lyons (2011) offered several critiques of the social network analyses of Christakis and Fowler, including issues of confounding, model inconsistency, and statistical dependence in networks. Here we show that in some settings, social network analyses of the type employed by Christakis and Fowler will still yield valid tests of the null of no social contagion, even though estimates and confidence intervals may not be valid. In particular, we show that if the alter's state is lagged by an additional period, then under the null of no contagion, the problems of model inconsistency and statistical dependence effectively disappear which allow for testing for contagion. Our results clarify the setting in which even "flawed" social network analyses are still useful for assessing social contagion and social influence.