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I am estimating a beta-regression using the logit-link function with a continuous dependent variable bound between 0 and 1 and 5 continuous predictor variables.

In R the equation is given by: betareg(y~ x1+ x2+ x3+ x4 + x5, link="logit", data=data), however I need to write out the equation with parameters in my paper, and I don't know how to do this.

Can anybody tell me how to write out the equation for my beta regression, and in turn how to interpret each parameter in the equation? If the information is needed; the beta-distribution of my dep var is given by alfa= 14,57 and beta=15,36.

Thank you very much in advance to anybody who can help!

Magnus Leschly
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    Suggest you start by explaining what you find unclear in the package documentation at https://cran.rstudio.com/web/packages/betareg/index.html. The vignette 'Beta Regression in R' is pretty good, & no point reproducing it here. – Scortchi - Reinstate Monica Jan 09 '22 at 10:22
  • Thank you for answering! The problem is that we are really not strong statisticians, so we have trouble translating the equations given in the vignette to our own model.

    In the vignette it says that the beta regression model can be defined as: g(µi) = xi*β = ηi

    Assuming that Y is beta distrubted given the paramaters µ, φ.

    Does this mean that we can write the systematic component of our model as: Y=B0 + B1X1 + B2X2 (…) B5+X5, as long as we specify that our Y is beta distributed?

    Further more we have trouble understanding when the Logit-link function comes in to the equation

     – Magnus Leschly Jan 09 '22 at 12:54
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    See https://stats.stackexchange.com/q/48594/17230 & the linked https://stats.stackexchange.com/q/20523/17230 for an explanation of how generalized linear models work, & the role of the link function. (Beta regression isn't a generalized linear model sensu stricto, but may as well be till you get into the fitting algorithm.) And if you edit your question to focus on any remaining doubts, you stand a very good chance of getting a satisfactory answer. – Scortchi - Reinstate Monica Jan 09 '22 at 13:18

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