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I fitted a beta regression model via MCMC with a complementary log-log link function. Is there a way to interpret it in a layman's terms?

The estimates of the model are:

\begin{align} \beta_0 &= -1.12 &\beta_1 &= -0.142 &\beta_2 &= 0.127 \\ \eta_0 &= -3.22 &\eta_1 &= 0.72 &\eta_2 &= 0.87 \end{align}

The response variable is the proportion of income spent on children's education, $X_1$ is the family income, and $X_2$ is the number of sons.

The $\beta$'s are associated with the mean parameter of the distribution and the $\eta$'s with the dispersion parameter.

I already read this topic interpreting estimates of cloglog logistic regression, but I think that that interpretation is not appropriate.

  • What exactly is not appropriate for you in the second question? – Tim May 30 '17 at 14:42
  • @Tim I think that the interpretation of parameters as hazard ratios not make sense for this problem, since it's not related with survival analysis. –  May 30 '17 at 14:44
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    @Roland I'm not aware of a "nice" interpretation that works in beta regression models. One could say, in your case, that the log-proportion not spent on children's education increases by about 13% per son. But this is clearly less intuitive than the log-survival from Glen_b's answer. – Achim Zeileis May 31 '17 at 21:55

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