Abstract:
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The hierarchical network model (HNM) is a framework introduced by Sweet, Thomas & Junker, (2013) and Sweet, Thomas & Junker (2014) for modeling interventions and other covariate e ects on ensembles of social networks, such as what would be found in randomized controlled trials in education research. In this paper, we develop calculations for the power to detect an intervention e ect using the hierarchical latent space model (HLSM), an important subfamily of HNMs. We derive basic convergence results and asymptotic bounds on power, showing that standard error for the treatment e ect is inversely proportional to the product of the number of ties and the number of networks; a result rather di erent from the usual e ect of cluster size in hierarchical linear models, for example. We explore these results with a simulation study and suggest a tentative approach to power for practical applications.
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