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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!

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  • $\begingroup$ One explanation you don't seem to have ruled out is random variation. If you observed a new data set for each, might your decisions have gone the other way? You might like to consider cross-validation $\endgroup$
    – Glen_b
    Commented Oct 17, 2013 at 7:16
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    $\begingroup$ Each of the link functions is an actual function whose value can be computed. Try looking up the formula for each of your links (for example, the logit is clearly defined on wikipedia), and then graph each function to see its "physical" meaning. $\endgroup$
    – zkurtz
    Commented Oct 17, 2013 at 12:15
  • $\begingroup$ Closely related: stats.stackexchange.com/questions/20523/… and $\endgroup$
    – Momo
    Commented Oct 19, 2013 at 15:25
  • $\begingroup$ Very helpful, thanks! I hadnt seen the other thread. $\endgroup$
    – Neodyme
    Commented Oct 21, 2013 at 2:27

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