Suppose that we have this output for Logistic Regression:
Coef EXP(Coef)
X1 2.45 11.67
X2 0.40 1.449
X3 -4.1401 0.0159
Here X3 has highest absolute Coefficient value but lowest EXP(coef) values.
* If we want ranking these variables based on importance we should rank based on Coef or EXP(Coef)?
* As we can see all Exp(Coef) are positive. How we can consider negative coefs here?
Thanks.
It is not possible to answer your question fully until you tell us something about the X's and how they are the measured ; what scale are they on: Eg is X1 binary and X3 continuous?. You also need to understand that under certain condition the EXP values are differential odds and a 1 is no effect but smaller AND larger values away from 1 are potentially big effects.. So an odds of 0.00159 is a major reduction in the odds ( ie protective from the event occurring) that is increasing X3 by 1 unit is lowering the odds hugely in this case - a vary large effect. The Logit Coeff Estimate and its exponentiated value are telling you the same thing : increase X2 by1 leads to a modest increase in the binary 'Yes' event of Y; increase X1 by1 leads to a very large increase; increase X3 by1 leads to a very large decrease. You would need to explain the substantive meaning of the variables to assess whether these very large effects are plausible.
In terms of size of effect you may wish to look at
https://www.researchgate.net/post/Any_advice_on_Associations_and_Odds_ratio_in_Epidemiological_studies/1
You may like to follow this free online course
http://www.bristol.ac.uk/cmm/learning/online-course/course-topics.html#m06
on the binary response regression model
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