Re: st: large coefficients in logistic regression

[Richard Williams <richardwilliams.ndu@gmail.com>]

At 04:27 PM 8/29/2011, Sabrina Helmut wrote:
> Dear all,
>
> I have a general question regarding large coefficients in logistic 
> regression. Is it possible that the estimated coefficients for a 
> specific variable in logistic regression is highly dependent on the 
> dimension of this variable. So, in my case the independent variable 
> ranges from -0.0009 and 0.1197 which results in a coefficient from 
> logistic regression that is 48.5. To my knowledge, such large 
> coefficients are uncommon for logistic regression. So, do you think 
> this is just due to these very small values for my dependent 
> variable and thus not a problem for my results? Thanks

I am not sure how you would define "large". You can make a 
coefficient bigger or smaller just by rescaling the X variable, e.g.

sysuse auto
reg price mpg
gen mpg2 = mpg * 100
reg price mpg2

In your case, the 48.5 coefficient tells you that a 1 unit increase 
in X would increase the log odds of the event occurring by 48.5. But, 
X only ranges from about 0 to .12, so a 1 unit increase is about 8 
times larger than anything you would actually observe. If you 
multiply X by 100, the variable will range from about 0 to 12 and the 
new coefficient will be .485.

How you scale an X is often pretty arbitrary. You may change the 
scaling for aesthetic reasons, e.g. you are getting a coefficient 
with a bunch of unsightly 0s at the beginning. Or, the model may have 
trouble converging because of the way X is scaled (even computers 
only have so much precision). I don't know what X is, but I would 
probably try to scale it so a 1 unit increase was something 
meaningful to me. But in any event, 48.5 (or 485, or 48500) wouldn't 
bother me unless I had other reasons for finding the number implausible.


-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
OFFICE: (574)631-6668, (574)631-6463
HOME:   (574)289-5227
EMAIL:  Richard.A.Williams.5@ND.Edu
WWW:    http://www.nd.edu/~rwilliam

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