Accuracy and power analysis of social networks built from count data

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 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 network correlation: the correlation between an estimated social network and its true network, using a Gamma–Poisson model of social event rates for networks constructed from count data. We use simulations to assess how the level of network correlation 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 social event rate and the harmonic mean of sampling times positively impacts the strength of network correlation. We also show that the required level of network correlation to achieve a given power level depends on many factors, but that 0.80 network correlation usually corresponds to around 80% power for nodal regression in ideal circumstances. We provide guidelines for using our network correlation estimator to verify the accuracy of networks built from count data, and to conduct power analysis. This can be used prior to data collection, in post hoc analyses or even for subsetting networks in dynamic network analysis. The network correlation estimator and custom power analysis methods have been made available as an r package.