Regression-based negative control of homophily in dyadic peer effect analysis

A prominent threat to causal inference about peer effects in social science studies is the presence of homophily bias, that is, social influence between friends and families is entangled with common characteristics or underlying similarities that form close connections. Analysis of social study data has suggested that certain health conditions such as obesity and psychological states including happiness and loneliness can spread between friends and relatives. However, such analyses of peer effects or contagion effects have come under criticism because homophily bias may compromise the causal statement. We develop a regression-based approach which leverages a negative control exposure for identification and estimation of contagion effects on additive or multiplicative scales, in the presence of homophily bias. We apply our methods to evaluate the peer effect of obesity in Framingham Offspring Study.