Log transformation of independent variable in logistic regression

[Kjell Weyde]

Dear Statalist users,

I have a logistic regression model where the exposure is concentration of a metal (Cu) in blood. Such exposures are typically log transformed, as is the case in my analysis (natural log). However, when I look at the output, the OR and 95% CI seem blown up:

Logistic regression                             Number of obs     =      1,057
                                                LR chi2(10)       =     104.01
                                                Prob > chi2       =     0.0000
Log likelihood = -336.15374                     Pseudo R2         =     0.1340

----------------------------------------------------------------------------------
              CP | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-----------------+----------------------------------------------------------------
           logCu |   28.24988     18.772     5.03   0.000     7.680589    103.9055

The residual plot looks like this:


I also tried with Cu untransformed, which I think looks better:

Logistic regression                             Number of obs     =      1,057
                                                LR chi2(10)       =     104.23
                                                Prob > chi2       =     0.0000
Log likelihood = -336.04232                     Pseudo R2         =     0.1343

----------------------------------------------------------------------------------
              CP | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-----------------+----------------------------------------------------------------
         Cu_ug_L |   1.002026   .0004019     5.05   0.000     1.001238    1.002814

Residual plot:


How to decide whether to log transform or not?


Best,
Kjell Weyde

[Joseph Coveney]

To me, the statistics side doesn't tell you anything. They look pretty much the same, and so no help there.

What does the subject matter side tell you?