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# Re: st: ZOIB procedure

 From Maarten Buis To statalist@hsphsun2.harvard.edu Subject Re: st: ZOIB procedure Date Mon, 19 Sep 2011 15:43:34 +0200

```On Mon, Sep 19, 2011 at 3:12 PM, Cameron McIntosh wrote:
> For proportions, Warton et al. (2011) recommend a logit transformation to achieve linearity. You could then run a linear model in -gllamm-, while allowing cov(e1,e2) and back-transform the predicted values (yhats).

You do not have to use -gllamm- for that, use -mvreg- instead. In that
case you are using Aitchison's (2003) method.

> Exponentiating these should return the geometric mean value of the yhats, and the geometric mean and median are (asymptotically) equivalent.

That is not quite correct, you will get the geometric mean if you log
transform your dependent variable, and afterwards exponentiate the
mean. With the logit transformation the back-transform is fairly
meaningless. See the example below:

*------------ begin example ----------------
sysuse auto, clear
sum price, meanonly
gen pprice = (price - r(min) ) /(r(max) - r(min))
gen logit = logit(pprice)
gen log = ln(pprice)

ameans pprice
sum  logit, meanonly
di invlogit(r(mean))
sum log, meanonly
di exp(r(mean))
*------------ end example ----------------
(For more on examples I sent to the Statalist see:
http://www.maartenbuis.nl/example_faq )

-- Maarten

Aitchison (2003) The Statistical Analysis of Compositional Data.
Caldwell, NJ: The Blackburn Press.

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany

http://www.maartenbuis.nl
--------------------------

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```