Control and estimation on large-scale social networks often necessitate the availability of models for the interactions amongst the agents in the network. However characterizing accurate models of social interactions pose new challenges due to their inherent complexity and unpredictability. Moreover, model uncertainty on the interaction dynamics becomes more pronounced for large-scale networks. For certain classes of social networks, in the meantime, the layering structure allows a compositional approach for modeling as well as control and estimation. The layering can be induced in the network, for example, due to the presence of distinct social types and other indicators, such as geography and financial ties. In this paper, we present a compositional approach to determine performance guarantees on layered networks with inherent model uncertainties induced by the network. To this end, we use a factorization approach to determine robust stability and performance of the composite network based on a layered control mechanism. This is accomplished by a layered cost-guaranteed design that is subsequently shown to be solved via a layered Riccati-type solver, mirroring the network structure. We provide an example of the proposed methodology in the context of opinion dynamics on large scale social networks.