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


From   Austin Nichols <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Interpretation of log transformed variables in logistic regression?
Date   Fri, 6 Feb 2009 11:22:03 -0500

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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