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Re: st: RE: retransformation of ln(Y) coefficient and CI in regression


From   Nick Cox <njcoxstata@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: retransformation of ln(Y) coefficient and CI in regression
Date   Mon, 6 Jun 2011 07:14:00 +0100

prediction +/- favoured multiplier * standard error.

Nick

On Sun, Jun 5, 2011 at 5:55 PM, Steve Rothenberg <drlead@prodigy.net.mx> wrote:
> Thank you for the glm suggestion, Nick.
>
> After
>
> . glm Y i.factor, vce(robust) family(Gaussian) link(log)
>
> followed by
>
> . predict xxx, mu
>
> the command does indeed return the factor predictions in the original Y
> metric.
>
> However, the regression table with 95% CI is still in the original ln(Y)
> units and I am still stuck not being able to calculate the 95% CI in the
> original Y unit metric.  The predict command for returning prediction SE
> (stdp) also only returns the SE in the ln(Y) metric.
>
> I've read the manual on glm postestimation and can derive no hints on this
> issue.
>
> I'd welcome further suggestions for deriving the 95% confidence interval in
> the original Y metric after either
>
> . regress ln(Y) ..., vce(robust)
>
> or
>
> . glm Y ..., link(log) vce(robust)
>
> or any other estimation commands.
>
> Steve Rothenberg
> ****************
>
> If you recast your model as
>
> glm Y i.factor ... , link(log)
>
> no post-estimation fudges are required. -predict- automatically supplies
> stuff in terms of Y, not ln Y.
>
> Nick
> n.j.cox@durham.ac.uk
>
> -----Mensaje original-----
> De: Steve Rothenberg [mailto:drlead@prodigy.net.mx]
> Enviado el: Sunday, June 05, 2011 10:27 AM
> Para: 'statalist@hsphsun2.harvard.edu'
> Asunto: retransformation of ln(Y) coefficient and CI in regression
>
> I have a simple model with a natural log dependent variable and a three
> level factor predictor.    I’ve used
>
>  . regress lnY i.factor, vce(robust)
>
> to obtain estimates in the natural log metric.  I want to be able to display
> the results in a graph as means and 95% CI for each level of the factor with
> retransformed units in the original Y metric.
>
> I’ve also calculated geometric means and 95% CI for each level of the factor
> variable using
>
> . ameans Y if factor==x
>
> simply as a check, though the 95% CI is not adjusted for the vce(robust)
> standard error as calculated by the -regress- model.
>
> Using naïve transformation (i.e. ignoring retransformation bias) with
>
> . display exp(coefficient)
>
> from the output of -regress- for each level of the predictor, with the
> classic formulation:
>
> Level 0 = exp(constant)
> Level 1 = exp(constant+coef(1))
> Level 2 = exp(constant+coef(2))
>
> the series of retransformations from the -regress- command is the same as
> the geometric means from the series of -ameans- commands.
>
> When I try to do the same with the lower and upper 95% CI (substituting the
> limits of the 95% CI for the coefficients) from the -regress- command,
> however, the retransformed IC is much larger than calculated from the-
> ameans- command, much more so than the differences in standard errors from
> regress with and without the vce(robust) option would indicate.
>
> I’ve discovered -levpredict- for unbiased retransformation of log dependent
> variables in regression-type estimations by Christopher Baum in SSC but it
> only outputs the bias-corrected means from the preceding -regress-.  To be
> sure there is some small bias in the first or second decimal place of the
> mean factor levels compared to naïve retransformation.
>
> Am I doing something wrong by treating the 95% CI of each level of the
> factor variable in the same way I treat the coefficients without correcting
> for retransformation bias?  Is there any way I can obtain either the
> retransformed CI or the bias-corrected retransformed CI for the different
> levels of the factor variable in the original metric of Y?
>
> I'd like to retain the robust SE from the above estimation as there is
> considerable difference in variance in each level of the factor variable.
>

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