I recently read a paper in which an academic compared two competing models of voting theory. One of the advanced diagnostic tests he did was to try and see whether either of the models could "formally encompass one another". The way he was able to interpret the results was by comparing the reduction in residual deviance or AIC when M1 was added to M2, as opposed to M2 being added to M1.
I have joylessly been trying to do this in R. Does anybody have any experience with encompassing tests? Effectively all I am attempting to do is compare two models which are non-nested. The models are completely different apart from the control variables, therefore anova(m1, M2) does not work.
Can anyone advise or suggest ways to proceed?