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I'm trying to understand some of my data in a logistic regression. I plotted headache (yes/no) vs. age and get an OR of 0.95.

Now I realize this means that for every year 'younger', you have a 0.95 less odds of having headache.

But I want to convert this into something people (and I) understand. How do I convert this to probabilities? Would I need to create age groups and then somehow convert the OR to RR?

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  • $\begingroup$ You are interested in the derivative of probability with respect to the independent variable. For logistic regression, this is usually referred to as the "marginal effect." You can calculate marginal effects, but unlike with linear regression it is not a unique constant. $\endgroup$
    – Matt P
    Commented Apr 9, 2019 at 19:06

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The problem with converting odds ratios into risk differences is that the risk difference for a 1-unit change in age depends on the level of age. This is because logistic regression is a nonlinear model. It is linear in the log odds but nonlinear in the probability.

To get risk differences at each level of age, you need to use a marginal effects procedure (e.g., margins in Stata) or a model that is parameterized in terms of the risk difference (e.g., binomial regression with an identity link, aka the linear probability model). You can also plot the predicted probability at each level of age and simply present the plot as a summary of the results.

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