From: Tobias Verbeke <tobias.verbeke_at_telenet.be>

Date: Wed, 16 Apr 2008 20:00:10 +0200

*>
*

> [...]

*>
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*> Confidence interval for the mean of Y? If that is the case, when you
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*> transformed Y to logY and run a regression assuming normal deviates you
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*> were in fact assuming that Y distributes lognormally. Your interval must
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*> be assymetric, reflecting the shape of the lognormal. The lognormal
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*> mean is lambda=exp(mu + 0.5*sigma^2), where mu and sigma^2 are the
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*> parameters of the normal variate logY. A confidence interval for lambda is
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*> Lower Bound=exp(mean(logY)+0.5*var(logY)+sd(logY)*H_alpha/sqrt(n-1))
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*> Upper Bound=exp(mean(logY)+0.5*var(logY)+sd(logY)*H_(1-alpha)/sqrt(n-1))
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*> where the quantiles H_alpha and H_(1-alpha) are quantiles of the
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*> distribution of linear combinations of the normal mean and variance
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*> (Land, 1971, Ann. Math. Stat. 42:1187-1205, and Land, 1975, Sel. Tables
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*> Math. Stat. 3:385-419).
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*> Alternatively, you can model directly
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*> Y=p1*X^p2, p1=exp(your alpha), p1=beta
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*> with a lognormal likelihood and predict the mean of Y with the fitted
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*> model (I'm guessing here).
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*> It could be useful to check Crow and Shimizu, Lognormal distributions.
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*> Theory and practice, 1988, Dekker, NY.
*

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https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Wed 16 Apr 2008 - 18:02:38 GMT

Date: Wed, 16 Apr 2008 20:00:10 +0200

Rubén Roa-Ureta wrote:

> tom soyer wrote:

>> Hi >> >> I have a general statistics question on calculating confidence interval of >> log transformed data. >> >> I log transformed both x and y, regressed the transformed y on transformed >> x: lm(log(y)~log(x)), and I get the following relationship: >> >> log(y) = alpha + beta * log(x) with se as the standard error of residuals >> >> My question is how do I calculate the confidence interval in the original >> scale of x and y? Should I use

> [...]

For the record, I'm working on a package to deal with these problems at

http://r-forge.r-project.org/projects/lognorm/

I uploaded a very first function lnormCI to
the svn repository a few minutes ago;

Be cautious, though: it is pre-alpha and I
know there is a problem with at least one
of the methods implemented (haven't worked
on it since 5 months or so).

Regards,

Tobias

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https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Wed 16 Apr 2008 - 18:02:38 GMT

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