variance vs. standard deviation in beta regression

I have modeled a relationship using beta-regression in the betareg package for R. I can predict values and associated variances of those predictions using the predict function in R. I'd like to convert these variances to standard deviations. This seems striaghtforward, just take the square root of the variance. However, there is an issue with this. First, the standard deviation is larger than the variance in beta regerssion, since the variance is always less than 1, and the square-root of a value less than 1 is always larger than the initial value. Second, and more concerning, when I convert to standard deviation by taking the square root of the variance, I get confidence intervals that overlap 0 and 1. This is a problem, because by its very nature beta-regression is designed to model values on the interval (0,1). Uncertainties beyond 0 and 1 are nonsensical.

How can I go about calculating standard deviation from a variance estimate from a beta-regression model, such that the standard deviation envelope will never be less than 0 or greater than 1?

• How did you calculate your confidence intervals? Aug 18 '16 at 16:58
• @Glen_b the confidence intervals I'm plotting are either +/- the variance or +/- the standard deviation (as I have calculated it). Aug 18 '16 at 18:57
• Sorry I called it a confidence interval, thinking it was an interval for the mean but on re-reading it might be a prediction interval you seek. Can you clarify what you're forming an interval for? Is it a pointwise interval? Can you clarify your calculation of the variance or the standard deviation? Aug 18 '16 at 22:58
• In either the case of forming a CI for the mean or for a prediction, adding and subtracting multiples of the standard deviation won't be quite correct - even assuming you get the right standard deviation - for beta regression. Using variance is really wrong -- it isn't even in the right units. Please edit your question to clarify what you actually did as well as what you're attempting to get Aug 18 '16 at 23:01