The regular research has had interesting results like showing a distinct pattern of cognitive traits and values associated with libertarian politics, but there's no reason one can't use it for investigating LWers in more detail; for example, going through the results, "we can see that many of us consider purity/respect to be far less morally significant than most", and we collectively seem to have Conscientiousness issues. (I also drew on it recently for a gay marriage comment.) If there were more data, it might be interesting to look at the results and see where LWers diverge the most from libertarians (the mainstream group we seem most psychologically similar to), but unfortunately for a lot of the tests, there's too little to bother with (LW n<10). Maybe more people could take it.
Big 5: http://www.yourmorals.org/bigfive_process.php
(You can see some of my results at http://www.gwern.net/Links#profile )