A couple of weeks ago, I wrote a blog post about modeling ideal points of US senators. I wanted to follow up (very briefly), since I was curious about comparing the Bayesian method there with Principal Component Analysis (PCA).
Here are the (new) results performing PCA on the voting record:
Here are the (older) results using ideal point modeling:
It’s interesting to compare the methods (the scale on the x-axis is irrelevant). Both models do a good job of capturing the more moderate senators, since Susan Collins, Lisa Murkowski, and Kelly Ayotte are in the middle in both methods. The furthest left senator using PCA is Maria Cantwell, who is also pretty far left with ideal points. Meanwhile, the furthest right senator with PCA is Tom Coburn (whose Wikipedia page describes him as “the godfather of the modern conservative, austerity movement”), yet he is further left than 8 senators with ideal point modeling.
Overall, I was surprised by how similar these results were, given how differently the two methods are motivated. Ideal point modeling yields scores for every bill and senator (along with a predictive interpretation), while PCA can reduce the voting data to any dimension to capture senator voting habits (not to mention it’s much faster). I would definitely be interested in exploring these methods with more rigor.