jandresgannon
commented
6 years ago It does make sense. Let's each do some reading on polynomial and non-linear regression to see how folks do it and what potential problems arise.
If we can find another quant IR paper that has done any model with a bimodal or non-monotonic distribution that will help a lot. The network part of our paper benefited from being able to model the Ward and Dorussen's network centrality stuff in the UN peacekeeping paper, so we just need something analogous.
The curvilinear hypothesis does not lend itself well to linear models. Technically speaking, in the paper we test for the scope conditions that need to be met if our theory is right -- aligned states commit more than non-aligned ones. But we don't actually test the more nuanced "room to gain security guarantees" hypothesis, because the expected utility function's peak is in the middle of the x-axis, not the end.
One way to better fit the data is through a generalized additive model. But fitting a GAM does not provide coefficient estimates, it is just predictive and any p-values relate to the need for a GAM. A better path might be to compare various model specifications (polynomial vs linear vs different polynomial) and to train these models on the first few years (2001-2003). We can then see which model performs best on 2004 and 2005 (maybe include 2006). If the polynomial structure that best fits our theory also performs best out of sample, then that serves as a means of testing our hypothesis.
Otherwise we might just run into critiques that we are just fitting to noise and not actually testing our hypothesis...
@jandresgannon does this make sense?