I am performing ordinal regression on several datasets, I have 5 ordered response categories and only one explanatory variable X. For each dataset I run the analysis 3 times, each time using a different link function (1. probit, 2. logit, 3. comploglog) and I calculate the AIC to see which function fits my data best.
It seems that for different datasets I get different link functions significantly providing a "best" fit; for example probit is better for dataset 1 and logit is better for dataset 2 etc. I am trying to find an explanation for such difference.
So my question is, what is the "physical" meaning of each link function? For example, I understand the probit link function assumes the response scale can be related to a latent continuous, normally distributed variable but for the other 2 I have no idea.
Any insight on this would be great!