Social networks, wherein the edges represent nonbehavioral relations such as friendship, power, and influence, can be difficult to measure and model. A powerful tool to address this is cognitive social structures (Krackhardt, D. (1987). Cognitive social structures. Social Networks, 9(2), 109–134.), where the perception of the entire network is elicited from each actor. We provide a formal statistical framework to analyze informants’ perceptions of the network, implementing a latent space network model that can estimate, e.g., homophilic effects while accounting for informant error. Our model allows researchers to better understand why respondents’ perceptions differ. We also describe how to construct a meaningful single aggregated network that ameliorates potential respondent error. The proposed method provides a visualization method, an estimate of the informants’ biases and variances, and we describe a method for sidestepping forced-choice designs.