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Thank you, Jay, for the interesting reference.I'd be interested in
receiving your SAS code, if you are willing to share. I will have to
think hard about the assumptions that I want to make (distributional
assumptions, as well as the diminishing returns issue), and see where
it gets me. Lots to think about.
Thanks,
Eva
2009/4/2 Verkuilen, Jay <[email protected]>:
> I've been working on a paper for random effects modeling of
> conditionally beta random variables which I am going to be diving into
> again in the next few weeks (finally!). We don't have code for Stata but
> I can send you SAS code (or winBUGS scripts for Bayesian versions). Also
> see:
>
> Z. Qiu, P. Song, & M. Tan (2009). Simplex Mixed-Effects Models for
> Longitudinal Proportional Data. Scandanavian J. Stat. 35(4): 577-596.
>
> This paper proposes using the simplex distribution for the error
> density, with the multivariate Gaussian as the mixture. (The simplex
> distribution is to the inverse Gaussian what the beta is to the gamma.)
> There are many other such distributions and at this point I really don't
> have a clue as to what distribution on a bounded interval is better.
>
> Anyhow, my feeling is that if the Tobit approach is working and giving
> sensible answers, and if you're comfortable with the linearity
> assumptions inherent in it as opposed to the diminishing returns near
> the boundary assumption inherent in the nonlinear models, I'd stick with
> it. If you feel there should be diminishing returns as you get close to
> the boundary the nonlinear model makes sense. For many models, you can
> "cheat" them back into the unit interval quite safely, e.g., by
> rescaling all the observations as:
>
> Ynew = eps/2 + (1-eps/2)*Yold
>
> without disturbing estimation and inference much. (However, the
> logit-transformed normal is not one of these models.)
>
> JV
>
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