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I'd like to make sure I'm interpreting average marginal effects for categorical and continuous variables correctly (interpretation of binary variables seems straightforward).

Using Stata, I ran a logistic regression to model a binary outcome as a function of Census region (1 = Northeast, 2 = Midwest, 3 = South, and 4 = West) and age category (values 1-5; modeled as a continuous variable). Northeast is the reference category for region.

logistic outcome i.region agecategory

  1. Categorical variable - using this Stata code...

    margins, dydx(region)
    

Stata provides an average marginal effect of 0.1 for South (region = 3) vs Northeast (region = 1). Does this mean that the difference between the predicted probability of the outcome is 0.1 percentage points when assuming everyone has a value of region = 3 vs region = 1 (holding age category at its observed value)?

  1. Using this Stata code...

    margins, dydx(agecategory)
    

Stata provides an average marginal effect is 0.5. Does this mean that the change in predicted probability of the outcome is 0.5 percentage points for all possible one-unit increments in agecategory: 2 vs 1, 3 vs 2, 4 vs 3, 5 vs 4?

Thanks.

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  • $\begingroup$ Could you re-write your post a bit to make it more clear what your actual question is? If I understand correctly, it's something like "how does Stata calculate the difference in predicted probabilities?" But I'm not quite sure :) $\endgroup$ – MyStackRunnethOver Mar 18 at 23:26
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Stata provides an average marginal effect of 0.1 for South (region = 3) vs Northeast (region = 1). Does this mean that the difference between the predicted probability of the outcome is 0.1 percentage points when assuming everyone has a value of region = 3 vs region = 1 (holding age category at its observed value)?

Yes. More precisely, it gives the average of each individual difference, since the effect varies with the age category.

Stata provides an average marginal effect is 0.5. Does this mean that the change in predicted probability of the outcome is 0.5 percentage points for all possible one-unit increments in agecategory: 2 vs 1, 3 vs 2, 4 vs 3, 5 vs 4?

No. The effect of the variable on the probability is not assumed to be linear in a logit. It will vary across observation with the value of the age category and of the other variable.

It calculates the average marginal effect, that is, the average change in the probability among all observation in the sample.

If you want to look at how this predicted effect changes at different values of the agecategory, you can use the at option of the margin command.

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