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If I standardize the coefficients (scale() command in R) of a beta regression with a logit link, how do I interpret them? I would say:

Of how many standard deviations (SD) the log odds of the y changes for a one SD increase in the covariates.

But is this correct?

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Standardizing the coefficients $\beta_1, \dots, \beta_k$ with scale() does not make sense. This would subtract the mean and divide by the standard deviation across the coefficients: $\tilde \beta_j = (\beta_j - \bar \beta)/\mathrm{SD}(\beta_1, \dots, \beta_k)$.

Multiplying $\beta_j$ with the standard deviation of the corresponding regressor $\mathrm{SD}(x_j)$ would have the same effect as standardizing the regressor $x_j$ (e.g., with scale()). This makes sense if you want to capture the marginal effect of a one standard deviation change in $x_j$ as opposed to a one unit change in $x_j$.

Additionally, you might find this answer about interpretation of betareg coef useful.

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  • $\begingroup$ To clarify, does this mean that multiplying the beta coefficient by the standard deviation of the predictor gives you a standardized beta that is comparable with standardized coefficients from other types of regression models, e.g. GLMs? $\endgroup$
    – qdread
    Sep 6, 2018 at 13:51
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    $\begingroup$ Yes, this behaves the same way as other models based on linear predictors. $\endgroup$
    – Achim Zeileis
    Sep 6, 2018 at 23:54

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