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Re: st: large coefficients in logistic regression


From   Richard Williams <richardwilliams.ndu@gmail.com>
To   statalist@hsphsun2.harvard.edu, <statalist@hsphsun2.harvard.edu>
Subject   Re: st: large coefficients in logistic regression
Date   Mon, 29 Aug 2011 17:55:47 -0500

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.


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Richard Williams, Notre Dame Dept of Sociology
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