Theoretical expectations regarding the legislative influence of outside agents, such as lobbyists, agency officials or policy experts, often depend on the relationship between legislators' and agents' preferences. Non-elected agents, however, typically will have preferences defined on a dimension that is different from that of elected legislators. I develop a bridging method that accommodates when the agent preference space shifts and rotates relative to the legislator roll-call preference space, and that identifies distances across the two dimensions in meaningful units necessary to test institutional hypotheses. In my application to Medicare hearings, I show that the agent preference space has an orthogonal rotation anchored by a quality-cost latent dimension, and that legislators heavily condition their questioning of agents on preference distance in a way consistent with informational models of lobbying.