Interpreting odds ratios in terms of standard deviation

[AMIRA ELASRA]

Hi,

I ran a glm model with a log link and the exp(b) (odds ratio) of the independent var x=1.007, which means that a 1 unit increase in x is associated with an increase in the predictive mean of y by 0.7% (PLEASE CORRECT ME IF I AM WRONG).

Now if i want to explain this relationship in terms of standard deviation knowing that std dev of x =8, then would it be correct to multiply 1.007 by 8(1.007*8=8.056)? if it is correct, can we say that 1 standard deviation increase in x is associated with ((8.056-1)*100)=705.6%) increase in the predictive mean of y?

Thx

[Clyde Schechter]

I ran a glm model with a log link and the exp(b) (odds ratio) of the independent var x=1.007, which means that a 1 unit increase in x is associated with an increase in the predictive mean of y by 0.7% (PLEASE CORRECT ME IF I AM WRONG).

That is correct.

Now if i want to explain this relationship in terms of standard deviation knowing that std dev of x =8, then would it be correct to multiply 1.007 by 8(1.007*8=8.056)? if it is correct, can we say that 1 standard deviation increase in x is associated with ((8.056-1)*100)=705.6%) increase in the predictive mean of y?

That is incorrect. A change of 8 (= 1 std dev) in x would be associated with an increase by a factor of 1.007^8 in the predictive mean, which is approximately 1.057), so a 5.7% increase.

That said, unless the variable x has no natural units, stating it in terms of the standard deviation of x, instead of a unit incraese in x, is likely to be more confusing than helpful.

[AMIRA ELASRA]

Thanks SO MUCH.

I understand your concern about the units of x. well the thing is that x is an index which was constructed by standardizing (mean=0, std dev=1) a number of variables Zs and then summing them to be=x. so x is not measured in standard deviation units as far as i understand (CORRECT ME IF I AM WRONG). so in order to make it more understandable, i thought i should explain the exp(b) in terms of standard deviation. Do you think it is a good approach? any other suggestions?

thx again

[Clyde Schechter]

Well, this sounds like a case where x, indeed, has no natural units, and a 1-unit change in x has no real meaning, so doing it in standard deviation units probably won't do any harm.

[AMIRA ELASRA]

Thanks a lot Clyde