My thesis is based on GAM and GLM. But my dependent variable is a proportion, meaning that $y \in (0,1)$ then I thought a better fit for this was the beta regression but this one is not considered in the GLM. What other distribution can I use for this dependent variable? I used the normal with the link function identity and log but I need another one to make a comparison.

  • $\begingroup$ Does it have to be a GLM sensu stricto? GLM-like algorithms are available for beta regression, for example in the betareg package for R. A GAM version is avialable in the mgcv package via family betar. $\endgroup$ – Reinstate Monica - G. Simpson Nov 28 '19 at 18:47
  • $\begingroup$ Yes, my thesis is a GLM vs GAM. But technically I can't use the beta uniparametric because is not with the exponential family. $\endgroup$ – Lexie Walker Nov 28 '19 at 22:35
  • $\begingroup$ I'm assuming that you don't have the sample total counts, that this is a true proportion? If so (true proportion) perhaps the quasi-binomial familyl, where you're just assuming a mean and variance relationship would be OK? $\endgroup$ – Reinstate Monica - G. Simpson Nov 29 '19 at 15:32
  • $\begingroup$ Actually my proportion is days a person took a medicine in a month, so technically is a count proportion. $\endgroup$ – Lexie Walker Dec 1 '19 at 0:03
  • $\begingroup$ Then you might model the data as binomial counts. You'll need to see how your software wants such data provided; R for example has several ways in which you can specify the sample totals or the positive (took a pill) and negative counts etc. $\endgroup$ – Reinstate Monica - G. Simpson Dec 2 '19 at 16:44

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