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st: Interpretation of log transformed variables in logistic regression?

Jason Davis-4
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.

Jason

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

Martin Weiss-5

<>

"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."


Quite apart from the log transformation prob, careful with those marginal
effects. "Marginal" means for a small change so you cannot extrapolate that
to a huge increase like your 1000 bucks... Also, -mfx- stresses the fact
that the impact will be different depending on the value the covariates take
on. As As default, the mean is assumed but you can ask for other evaluation
points...


HTH
Martin


-----Urspr√ľngliche Nachricht-----
Von: [hidden email]
[mailto:[hidden email]] Im Auftrag von Jason Davis
Gesendet: Freitag, 6. Februar 2009 16:19
An: [hidden email]
Betreff: st: Interpretation of log transformed variables in logistic
regression?

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.

Jason

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

Austin Nichols
In reply to this post by Jason Davis-4
Jason Davis <[hidden email]>:
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 <[hidden email]> 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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Re: st: Interpretation of log transformed variables in logistic regression?

Jason Davis-4
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 <[hidden email]>:

> Jason Davis <[hidden email]>:
> 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  
> <[hidden email]> 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.
> *
> *   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/
>



--
Jason Davis
PhD candidate in Geography
University of California, Santa Barbara
[hidden email]


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