Re: st: Inverse hyperbolic sine transformation

 From Austin Nichols <[email protected]> To [email protected] Subject Re: st: Inverse hyperbolic sine transformation Date Fri, 29 Jan 2010 14:08:22 -0500

```Stephane Mahuteau <[email protected]>:
If you are willing to assume homoskedastic errors, you can get
consistent estimates of the predicted outcomes y conditional on X
using the "smearing" estimator proposed by Duan
(http://www.jstor.org/stable/2288126).  If you are doing this because
you have a nonnegative skewed dependent variable, you are better off
with -poisson- or another model in that family, which will give you
much better estimates of the predicted outcomes conditional on X,
directly, with no additional work associated with back-transformation.
You can also get estimates of y conditional on X and y>0. What does
your model look like?  What are the X and y variables?

On Fri, Jan 29, 2010 at 12:06 PM, Maarten buis <[email protected]> wrote:
>
> --- 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
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