Longitudinal analysis of large social networks: Estimating the effect of health traits on changes in friendship ties

We develop novel mixed effects models to examine the role of health traits on the status of peoples' close friendship nominations in the Framingham Heart Study. The health traits considered are both mutable (body mass index (BMI), smoking, blood pressure, body proportion, muscularity, and depression) and, for comparison, basically immutable (height, birth order, personality type, only child, and handedness); and the traits have varying degrees of observability. We test the hypotheses that existing ties (i.e. close friendship nominations) are more likely to dissolve between people with dissimilar (mutable and observable) health traits whereas new ties are more likely to form between those with similar (mutable and observable) traits while controlling for persons' age, gender, geographic separation, and education. The mixed effects models contain random effects for both the nominator (ego) and nominated (alter) persons in a tie to account for the fact that people were involved in multiple relationships and contributed observations at multiple exams. Results for BMI support the hypotheses that people of similar BMI are less likely to dissolve existing ties and more likely to form ties, while smoker to non-smoker ties were the least likely to dissolve and smoker to smoker ties were the most likely to form. We also validated previously known findings regarding homophily on age and gender, and found evidence that homophily also depends upon geographic separation.