# st: RE: RE: interpretting log transformed co-efficients

 From "Lachenbruch, Peter" To Subject st: RE: RE: interpretting log transformed co-efficients Date Mon, 9 Feb 2009 08:36:24 -0800

```While the unbiased transform of the log mean is certainly appropriate (
to get unbiased estimates of the mean), one could also transform the
predicted values.  In this case, the percentiles will transform exactly.
In my dotage, I am finding I like to look at percentiles more and more -
especially with skewed data.

Tony

Peter A. Lachenbruch
Department of Public Health
Oregon State University
Corvallis, OR 97330
Phone: 541-737-3832
FAX: 541-737-4001

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Newson, Roger
B
Sent: Monday, February 09, 2009 3:34 AM
To: statalist@hsphsun2.harvard.edu
Subject: st: RE: interpretting log transformed co-efficients

If you are regressing a log-transformed outcome on one or more
X-variates using -regerss-, then you should probably use the -eform-
option. This implies that the coefficients displayed are geometric
means, or geometric mean ratios, or geometric mean per-unit ratios
(assuming an exponential relationship between the original untransformed
Y-variable and the X-variable. For instance, if the X-variable is female
gender, and the untransformed Y-variable is length of stay, then the
coefficient for female gender is the geometric mean ratio between length
of stay in females and length of stay in otherwise equivalent males.

This principle is explained in a Stata Tip in the Stata Journal (Newson,
2003). If you want the exponentiated intercept (equal in your case to
the geometric mean length of stay im males), then it is a good idea to
use the -noconst- option, and to define a second X-variate containing
values all equal to 1, whose coefficient is the exponentiated intercept.

I hope this helps.

Best wishes

Roger

References

Newson R. Stata tip 1: The eform() option of regress. The Stata Journal
2003; 3(4): 445.
http://www.stata-journal.com/article.html?article=st0054

Roger B Newson BSc MSc DPhil
Lecturer in Medical Statistics
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute
Imperial College London
Royal Brompton Campus
Room 33, Emmanuel Kaye Building
London SW3 6LR
UNITED KINGDOM
Tel: +44 (0)20 7352 8121 ext 3381
Fax: +44 (0)20 7351 8322
Email: r.newson@imperial.ac.uk
Web page: http://www.imperial.ac.uk/nhli/r.newson/
Departmental Web page:
genetics/reph/

Opinions expressed are those of the author, not of the institution.

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Ashwin
Ananthakrishnan
Sent: 08 February 2009 16:35
To: statalist@hsphsun2.harvard.edu
Subject: st: interpretting log transformed co-efficients

Hi,

I'm having some trouble interpretting the linear regression
co-efficients for log transformed variables.

I have outcomes (such as length of stay or costs) that are not normally
distributed, so I'm including the log transformed (now normal) variables
as the outcome measures in linear regression models.

But I'm not really sure how to interpret the resulting co-efficients. Do
they represent a % change in outcome for a defined change in a predictor
variable?

Just for example, suppose I'm modelling length of stay against gender
(male 0 female 1).

Without log transformation, if I get a linear regression co-efficient of
0.6, I can say that females have a 0.6 days longer stay.

But if I use log (length of stay) as the outcome and get a co-efficient
0.2 for the same linear regression model, how do I interpret this?

Thanks.

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
```