Finally had a moment to do the other parliaments for which I have data. Here they are. In each case the first plot is classic PCA and the second probabilistic:
The second axis is flipped in the PPCA plot – this happens in PCA – but it’s kind of interesting how there seem to be a selection of parties (PC, SDLP, SNP) on a line between Labour and the Lib Dems possibly representing a kind of political spectrum? There also seems to be a huge wasteland splitting the Tories from everyone else.
Labour appear a lot less coherent than in 1997 (just comparing the probabilistic plots, I don’t really trust the spread in the classic ones because of the missing value problem). Also, the line of small parties that seemed to link Lab and Lib Dem in 1997 has been pulled towards the Tories. (Again, ignore the 2nd axis flip).
2010 (only 49 divisions so far)
So, not much data yet – only 49 divisions (votes) – the effect of the coalition is clear and it looks like interesting groups may be developing between the Tories and Lid Dems (we would need more data to be sure of this). The coalition seems to have scared off the DUP (especially), PC and SNP who have all dramatically migrated towards Labour.
One criticism of this analysis is that PCA and PPCA both assume that the data are real-valued which is not the case for this data (each MP-vote pair is either -1, 1 or missing). I’ve been pointed in the direction of PCA-like techniques for binary data and will post some results ar some point if I can get it to go a bit faster (there’s quite a lot of data!).