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?