Abstract
Power analysis is used to estimate the probability of correctly rejecting a null hypothesis for a given statistical model and dataset. Conventional power analyses assume complete information, but the stochastic nature of behavioural sampling can mean that true and estimated networks are poorly correlated. Power analyses of animal social networks do not currently take the effect of sampling into account. This could lead to inaccurate estimates of statistical power, potentially yielding misleading results.
Here we develop a method for computing how well an estimated social network correlates with its true network using a Gamma-Poisson model of interaction rates. We use simulations to assess how the level of correlation between true and estimated networks affects the power of nodal regression analyses. We also develop a generic method of power analysis applicable to any statistical test, based on the concept of diminishing returns.
We demonstrate that our network correlation estimator is both accurate and moderately robust to its assumptions being broken. We show that social differentiation, mean interaction rate, and the harmonic mean of sampling times positively impacts the strength of correlation between true and estimated networks. We also show that the required level of correlation between true and estimated networks to achieve a given power level depends on many factors, but that 80% correlation usually corresponded to around 80% power for nodal regression.
We provide guidelines for using our network correlation estimator to verify the accuracy of interaction networks, and to conduct power analysis. This can be used prior to data collection, in post hoc analyses, or even for subsetting networks for use in dynamic network analysis. We make our code available so that custom power analysis can be used in future studies.
Competing Interest Statement
The authors have declared no competing interest.