Using retrospective sampling to estimate models of relationship status in large longitudinal social networks

• Estimation of statistical models for social networks is challenging.
• Dyads with no relationship (“null-dyads”) are common in large social networks.
• Propose to subsample the “always-null” dyads.
• Develop weighted likelihood Bayesian estimation method.
• Method enables large social networks to be analyzed feasibly and accurately.

Estimation of longitudinal models of relationship status between all pairs of individuals (dyads) in social networks is challenging due to the complex inter-dependencies among observations and lengthy computation times. To reduce the computational burden of model estimation, a method is developed that subsamples the “always-null” dyads in which no relationships develop throughout the period of observation. The informative sampling process is accounted for by weighting the likelihood contributions of the observations by the inverses of the sampling probabilities. This weighted-likelihood estimation method is implemented using Bayesian computation and evaluated in terms of its bias, efficiency, and speed of computation under various settings. Comparisons are also made to a full information likelihood-based procedure that is only feasible to compute when limited follow-up observations are available. Calculations are performed on two real social networks of very different sizes. The easily computed weighted-likelihood procedure closely approximates the corresponding estimates for the full network, even when using low sub-sampling fractions. The fast computation times make the weighted-likelihood approach practical and able to be applied to networks of any size.