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Re: st: Inverse hyperbolic sine transformation

From   Maarten buis <[email protected]>
To   [email protected]
Subject   Re: st: Inverse hyperbolic sine transformation
Date   Fri, 29 Jan 2010 17:06:52 +0000 (GMT)

--- On Fri, 29/1/10, Stephane Mahuteau <[email protected]> wrote:
> I estimated a double hurdle model using the Inverse
> Hyperbolic sine transformation to my dependent variable in
> the second hurdle. From these results I'd like to compute
> the expected values of this dependent variable y (given
> y>0) rather than using the expected values of the
> transformed variable. From what I read in the Cameron &
> Trivedi "Microeconometrics using stata" applied to some
> other transformations on non linear models, it looks like
> getting the expected values of the variable y from the
> estimated values of the transformed y would be more complex
> than just inversing the transformation. Would anybody have
> any idea on how I can perform this? Is it ok to just invert
> the transformation?

The problem is that that is a non-linear transformation. You
can easily see what happens in a simple model: predicting
the variable by its mean:

*-------- begin example ---------
sysuse nlsw88, clear
gen asinh_w = asinh(wage)
sum asinh_w
di sinh(r(mean))
sum wage
*-------- end example ------------

You can see here that first transforming the variable and
than backtransforming the mean, will not result in the mean
of the original variable. 

Probably the easiest solution to implement, but hard to 
explain to your audience, is that if you log transform
the dependent variable you could interpret the 
backtransformed predicted values as Geometric means. 
Alternatively, you can include the transformation as a 
link function in the likelihood, as happens in -glm-like 
models. Then you are modeling the mean directly, so the
predicted values do represent the conditional means.

Hope this helps,

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


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