On Thu, Dec 20, 2012 at 7:33 PM, Alan Acock <acock@me.com> wrote:
> If I run
>
>
> is there a clear interpretation of the coefficient or some transformation of the coefficients?
>
> I'm think the answer should be obvious to me, but it is not.
Having spent time developing a similar model (using the beta
distribution as an error with mixing terms, e.g., in Verkuilen &
Smithson, 2012) what I would say is that it's a logit scaled
coefficient. In general you could say it's a log-odds of some sort.
The transformed linear prediction usually fits much better than would
be an identity link formulation when there's reasonable skew and the
resulting predicted values are always admissible, but I agree that the
coefficients are not directly interpretable. That's not really all
that different than many other transformed coefficients in other GLMs
such as log link with gamma errors. That's one reason that I'd
recommend generating predicted values for meaningful scenarios, or
even entire predictive distributions.
Verkuilen, J. & Smithson, M. J. (2012). Mixed and Mixture Regression
Models for Continuous Bounded Responses Using the Beta Distribution.
Journal of Educational and Behavioral Statistics, 37(1), 82-113.
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