Measures
We focused on individuals who were assessed with the Center for Epidemiological Studies depression scale (CES-D) in 1983-2003 at times corresponding to the 5th, 6th, and 7th examinations of the offspring cohort. The median year of examination for these individuals was 1986 for exam 5, 1996 for exam 6, and 2000 for exam 7.
To test whether clustering of happy and unhappy people in the network is due to chance, we compared the observed clustering to the clustering in 1000 randomly generated networks in which we preserved the network topology and the overall prevalence of happiness but in which we randomly shuffled the assignment of the happiness value to each node.46 If clustering is occurring, then the probability that an alter is happy given that an ego is happy should be higher in the observed network than in the random networks. This procedure also allowed us to generate confidence intervals and measure how far, in terms of social distance, the correlation in happiness between ego and alters reaches.
Measures of centrality in networks capture the extent to which a node connects, or lies between, other nodes, and hence its tendency to be positioned near the centre of his or her local network. Centrality is also taken as a marker of importance. The simplest measure of centrality is a count of the number of friends (this is called “degree” centrality). People with more friends will tend to be more central. But this measure does not account for differences in the centrality of one’s friends. Individuals who are connected to many well connected peers are more central than those who are connected to an identical number of poorly connected peers. In other words, those who befriend popular people will tend primo messaggio su uniform dating to be more central than those who befriend the unpopular. We used eigenvector centrality to capture this aspect.47 This measure assumes that the centrality of a given person is an increasing function of the sum of all the centralities of all the people with whom he or she is connected (see appendix on bmj). Eigenvector centrality values are inherently relative: an individual connected to every other person in the network would have the maximum possible value, and a person not connected to anyone else would have a value of zero. In large networks, eigenvector centrality will not necessarily produce a measure of importance to the overall network but rather to a person’s local network. It is therefore possible that the most central individuals might not necessarily be located near the centre of a visualisation of the whole network-instead they will be located at the centre of their local networks.
Statistical analysis
The association between the happiness of individuals connected to each other, and the clustering within the network, could be attributed to at least three processes: induction, whereby happiness in one person causes the happiness of others; homophily, whereby happy individuals choose one another as friends and become connected (that is, the tendency of like to attract like)48; or confounding, whereby connected individuals jointly experience contemporaneous exposures (such as an economic downturn or living in the same neighbourhood13). To distinguish between these effects requires repeated measures of happiness,35 49 longitudinal information about network ties, and information about the nature or direction of the ties (for example, who nominated whom as a friend).
We evaluated regression models of ego happiness as a function of ego’s age, sex, education, and happiness in the previous exam, and of the happiness of an alter in the current and previous exam. Inclusion of ego happiness in the previous exam helps to eliminate serial correlation in the errors and also substantially controls for ego’s genetic endowment and any intrinsic stable predilection to be happy. Alter’s happiness in the previous exam helps to control for homophily.35 49 We evaluated the possibility of omitted variables or contemporaneous events or exposures in explaining the associations by examining how the type or direction of the social relationship between ego and alter affects the association between them. If unobserved factors drive the association between ego and alter happiness, then directionality of friendship should not be relevant. We also examined the possible role of exposure to neighbourhood factors by examining maps (see appendix on bmj).
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