We introduce a method for scaling two data sets from different sources. The proposed method
estimates a latent factor common to both datasets as well as an idiosyncratic factor unique to each.
In addition, it offers a flexible modeling strategy that permits the scaled locations to be a function
of covariates, and efficient implementation allows for inference through resampling. A simulation
study shows that our proposed method improves over existing alternatives in capturing the variation
common to both datasets, as well as the latent factors specific to each. We apply our proposed method
to vote and speech data from the 112th U.S. Senate. We recover a shared subspace that aligns with
a standard ideological dimension running from liberals to conservatives, while recovering the words
most associated with each senator’s location. In addition, we estimate a word-specific subspace that
ranges from national security to budget concerns, and a vote-specific subspace with Tea Party senators
on one extreme and senior committee leaders on the other.
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