# Interpreting link functions for hurdle gamma brms model

I am having some trouble interpreting the link functions for my hurdle gamma model, any help would be appreciated. My response variable is substance use. In my case, the link function for “mu” is log, the link function for “shape” is identity, and the link function for “hu” is identity. What are the mu estimates, the shape estimate and the hu estimate indicating ? Are the mu estimates the log of the probability that the response variable is 0 ?

Thank you!

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Hi,
`hu` is the probability that the response is exactly 0. Then with probability `1 - hu` the response is gamma distributed with mean `mu` and shape `shape`, which means the implied scale parameter of the gamma is `mu / shape`. If you use predictors for `hu` (i.e. if you have `hu ~ 1 + x` or similar in your formula), it will use logit link, so we basically have a logistic regression on `hu` the coefficients. If you don’t predict it, `brms` will just treat it as a parameter between 0 and 1 and the link function is not used.

For `shape` and `mu` the predictors are on the log scale. So coefficients for `mu` will generally correspond to multiplicative change in the outcome.

Does that resolve the confusion?

Best of luck with your model!

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Yes, thank you so much!