# Re: st: Interpretation of log transformed variables in logistic regression?

 From Jason Davis To statalist@hsphsun2.harvard.edu Subject Re: st: Interpretation of log transformed variables in logistic regression? Date Fri, 06 Feb 2009 17:48:22 -0800

```Thank you Austin, Martin and Massimo-

```
Upon further investigation, I found that I ahd lost most of my effective population when I failed to a add something to my zeros prior to log transforming them. Now my log odds ratios are near 1. All your explanations did help.
```
Ciao, Jason

Quoting Austin Nichols <austinnichols@gmail.com>:

```
```Jason Davis <jason_davis@umail.ucsb.edu>:
A one-unit increase in log income is a 172% increase in income, which
you estimate increases the odds of birth fivefold (a one-unit increase
in log income increases log odds by 1.68 so a one-percent increase in
income, or increase in log income of .01, increases log odds by
.0168).  If the odds of birth are .0204 at mean income, a one-percent
increase in income increases them to .0207 or so, according to your
estimates.  You have bigger problems--income is not exogenous, so an
exogenous increase in income might in fact have a very different
causal impact on the odds of birth than the one you estimate.  Perhaps
even a negative impact, rather than a positive one.

```
On Fri, Feb 6, 2009 at 10:19 AM, Jason Davis <jason_davis@umail.ucsb.edu> wrote:
```I can use some help with this one. I have run a multivariate logistical
regression with log transformed continuous variables, non-transformed
continous variables, and some categorical variables. The DV is birth outcome
in a given year (yes/no) and the IV of interest is income (log transformed).
The results are in odds ratios. My confusion is how do I interpret the odds
ratio of the log transformed continous variable. Specifically, the odds
ratio of log income is 5.4. If I back transform this I get 1.68. This does
not seem right, as a \$1 increase in income would raise the odds of giving
birth in a given year by 68%. This would mean \$1,000 raise would increase
the odds by 0.68*1000 or a 680% increase in the odds of giving birth. Any
suggestions would be greatly appreciated.
```
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```
```

--
Jason Davis
PhD candidate in Geography
University of California, Santa Barbara
jason_davis@umail.ucsb.edu

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