I'm trying to use Vuong's test to compare LR models - having trouble with the definition of 'strictly nonnested' vs 'partially nonnnested'/overlapping.
There are a few (lay language) definitions of ‘strictly non-nested’ floating around that suggest that models must be quite different to employ Vuong's [e.g...strictly nonnested if they have "different distributional assumptions on the errors, say normally or logistic distributed" or if they have "the same distributional assumption but different functional forms" such as if one is linear and the other is nonlinear”], but at the same time I see it used for testing models with "just" different parameters, i.e.
M1 <- glm(B1 + B2, family=binomial)
M2 <- glm(B3 + B4, family = binomial)
Vuongtest (M1, M2)
Any advice or reference appreciated. I myself cannot understand Vuong's paper but I did find this that looks like it contains a formal definition.
Can anyone comment?