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I have a very basic question on post-estimation for probit/logistic regression models (frequentist). The non-linear character of the link functions requires us to do post-estimation for a sensible interpretation of the coefficients. What is often suggested is to use predicted probabilities, marginal effects, and/or simulation-based methods.

I see the advantages of simulation methods as they allow us to include estimation uncertainty.

Are you aware of any reasons to prefer marginal effects over predicted probabilities or vice versa?

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Logistic regression results can be interpreted without post-estimation in terms of odds ratios. This is actually my prefered method.

It is common to include estimation uncertainty for marginal effects and predicted probability as well (typically using the delta method ), so that is not unique to the simulation approach.

When exploring the model results I would say that predicted probabilities and marginal effects are complementary: If you plot the predicted probability against an explanatory variable, then the marginal effect is the slope of that curve. When writing down the results, the relationship between the two is so close that you end up saying the same thing twice if you include both. So then you just choose the one you find easiest to explain, or is most commonly used in your sub-sub-sub-discipline.

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