Re: Contribution of each Variables in Logistic Regression
- From: jay <jayesh.srivastava@xxxxxxxxx>
- Date: Mon, 11 Jun 2007 12:44:43 -0000
On Jun 8, 9:47 am, DanCT <danmye...@xxxxxxxxxxx> wrote:
On Jun 7, 3:54 pm, mgl...@xxxxxxxxx wrote:
On Jun 1, 1:39 pm, jay <jayesh.srivast...@xxxxxxxxx> wrote:
How to quantify the contribution of each variables/covaraites in
logistic regression?
It sounds like a standardized logistic regression coefficient would
satisfy your needs. It turns out there are a number of ways to do
this, not all obvious. Here's one likely-looking source:
Menard, Scott. 2004. "Six approaches to calculating standardized
logistic regression coefficients."
American Statistician.
Regards,
Mike Lacy
Actually, the reason I did the simulation I mentioned before was to
compare the standardized estimates approach & wald chi-sq approach for
determining variable importance and contribution.
What I found was that, although they both have some degree of success,
chi-sq does a better job - especially in the presence of indicator
variables and/or correlated variables.
Jay, let me try to clarify my approach using a hypo. example that
includes a comparison of two categorical variables.
Suppose we have 3 variables that we are using to predict some Y:
1. Income -continuous
2. State -categorical
3. Gender -categorical
Then my regression analysis might look like:
{Intercept........Chisq = 5000}
Income ...........Chisq = 1000
I(State = NY).....Chisq = 700
I(State = CA).....Chisq = 200
I(Gender = Male)..Chisq = 100
I would rank the variables by Chisq (as I've already done).
Then note the total Chisq = 2000 (less the intercept). Then the
contribution of each variable would be the ratio to this total:
Income ...........Contrib = 50%
I(State = NY).....Contrib = 35%
I(State = CA).....Contrib = 10%
I(Gender = Male)..Contrib = 5%
Ranking is pretty much clear but still question remains what your
total chi square represent??
In any standard statistical techniques we first quantify how much
variation is there
for example in PCA we take the ratio of first eigen value and total
eigen value.
Here total chi square has no interpretation. If all the parameters
(Income -continuous,State -categorical, Gender -categorical)
are independent to each other then what you are saying makes sense.
.
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