If I use a GLM with the identity link, is there any difference to a linear model? For example, if I use a Gamma GLM with identity link and an Inverse Gaussian GLM with identity link, what is the difference from these to a linear model?

I've tried it in R and they give different coefficients, so I presume the models are different, but I don't see how.

  • $\begingroup$ A GLM models the expected value of a distribution conditional on a linear combination of the predictors. It should not be surprising that the expected value of a normal distribution and of a Gamma distribution are different. $\endgroup$
    – Roland
    Dec 10 '20 at 11:23