# Is it possible to extrapolate a percentage from given logistic regression coefficients?

If I have done a (binomial) logistic regression. Is it then possible from the coefficients to calculate a percentage of how much each of the variables affects the dependent variable.

Say that we have for example var1: 0.635, var2: 0.245, var3: 1.243. If we know that the depends variable Y in the data is 1 at 0.64 of the time. Can we then use this to calculated something a long the lines of:

Variable 1 has a 25% effect on Y, Variable 2 15%, and Variable 3 60%?

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It seems like you are asking a basic question as to whether or not one can compute an analog to R square from linear regression to logistic regression or perhaps more generally to the generalized linear model. The basis for this being possible with linear models is that that the total sum of squares can be separated into two non-overlapping sums of squares (model sum of squares and error sum of squares). But for generalized linear models R square does not carry through as a measure of goodness of fit for a model. The analog is the deviance which can be used to measure the effect of variables on the model by looking at the change in deviance when the variable is added to the model.

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I was thinking that since the coefficients indicate how much the odds ratio changes when the different variables are increased by 1 I should be able to use this to calculate some sort of percentage comparison between them. Say: If we have two variables we calculated that the probability of getting 1 increase from 0.64 to 0.70 if variable 1 is increased by one, and from 0.64 to 0.76 if variable 2 is increased. Then in a sense variable 2 has double the effect as variable 1 (0.12 compared to 0.06) and I'd like to say that it determines 66% of the probability and variable 1 33% of it... –  Stefan Andersson May 29 '12 at 11:30

Sounds like you are looking for something like relative risk or first differences. If so, calculate the predicted probability of observing a 1 with everything but your variable of interest set at its mean or median and your treatment at a low (or high) value, giving something like this

RR_rs = Pr(Y1 =r,Y2 =s|x1) / Pr(Y1 =r,Y2 =s|x)


Or first differences

FD_rs =Pr(Y1 =r,Y2 =s|x1)−Pr(Y1 =r,Y2 =s|x).


I suppose looking at some type of information criteria might partially get you what you want as well.

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