Lines between nodes indicate relationship (black for siblings, red for friends and spouses)

Lines between nodes indicate relationship (black for siblings, red for friends and spouses)

The generalised estimating equation regression models provide parameter estimates in the form of ? coefficients (as shown in the appendix on bmj), whereas the results reported in the text and in figures 4 ? and 5 ? are in the form of risk ratios, which are related to the exponentiated coefficients. We calculated mean effect sizes and 95% confidence intervals by simulating first difference in alter contemporaneous happiness (changing from 0 to 1) using 1000 randomly drawn sets of estimates from the coefficient covariance matrix and assuming all other variables are held at their means.52

We explored the sensitivity of our results by conducting numerous other analyses, each of which had various strengths and limitations but none of which yielded substantially different results from those presented here (see appendix on bmj).

The networks in this study, like those in all network studies, are only partially observed. Therefore, there will be measurement error in individual network attributes. For example, we measured a person’s centrality based on the observed social network, but that same person might be highly central to an unobserved network of individuals who did not take part in the study. If there is a correlation between this measurement error and happiness, it could bias our results. We evaluated this potential source of bias by measuring the Pearson correlation between the number of social relations named outside the Framingham Heart Study and subject happiness. The association was both small and not significant (?=?0.01, P=0.33),suggesting that the unobserved parts of the network do not bias the inferences we make within the observed network.

Results

Examination of the social network indicates that happy people tend to be connected to one another. Figure 1 shows the largest connected network component in 1996 and 2000 based on a restricted set of ties among siblings, spouses, and friends (coworker and neighbours are excluded to simplify the image). ? To highlight the clustering of happiness, each node is coloured according to the person’s happiness on a spectrum from blue (unhappy) to yellow (happy).

The clusters of happy and unhappy people seen in the network are significantly larger than expected by chance

Fig 1 Happiness clusters in the Framingham social network. Graphs show largest component of friends, spouses, and siblings at exam 6 (centred on year 1996, showing 1181 individuals) and exam 7 (year 2000, showing 1020 individuals). Each node represents one person (circles are female, squares are male). Node colour denotes mean happiness of ego and all directly connected (distance 1) alters, with blue shades indicating least happy and yellow shades indicating most happy (shades of green are intermediate)

The clusters of happy hookupdate.net/it/uberhorny-recensione and unhappy people seen in the network are significantly larger than expected by chance

Fig 1 Happiness clusters in the Framingham social network. Graphs show largest component of friends, spouses, and siblings at exam 6 (centred on year 1996, showing 1181 individuals) and exam 7 (year 2000, showing 1020 individuals). Each node represents one person (circles are female, squares are male). Node colour denotes mean happiness of ego and all directly connected (distance 1) alters, with blue shades indicating least happy and yellow shades indicating most happy (shades of green are intermediate)

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Figure 2 shows that the association between ego and alter happiness is significant up to three degrees of separation. ? A person is 15.3% (95% confidence interval 12.2% to 18.8%) more likely to be happy if a directly connected alter (distance 1) is happy. The effect for distance two alters is 9.8% (7.0% to 12.9%) and for distance three alters is 5.6% (2.4% to 9.0%).