Interpretation of marginal effects when model includes factor control variables

[Anja Heimann]

Hi,

I've been grippling with the interpretation of marginal effects in the presence of factor control variables for a while now and thought I'd ask here.

Basically, I am running a logistic regression and run margins like this

logit Employment age age_squared b1.Disability b1.Ethnicity b1.Sex b1.Disability#b1.Sex

margins b1.Disability#b1.Sex

Ethnicity is a factor variable with 5 categories, Disability and Sex have two categories each. Age and age_squared are continuous.

When I now get output that looks like this:

		Marginal Effect	Standard error
Gender/Disability	Male, Non-disabled	81.0	0.5
Gender/Disability	Male, Disabled	42.4	1.2
Gender/Disability	Female, Non-disabled	70.3	0.5
Gender/Disability	Female, Disabled	35.3	1.1

What I now don't know is what the 81 marginal effect means. If I didn't have the three control variables control variables, I would have thought the interpretation is that

non-disabled men are 81% likely to be in employment.

But how would I interpret it in light of ethnicity and the age variables I have in my model? The margins command holds them constant, I believe.

Can anyone help me out?

Many thanks

[Clyde Schechter]

No, it does not hold the ethnicity and age variables constant. It leaves them exactly as they are in the data.

So the interpretation is: if people all had the same joint distribution of age and ethnicity that are found in the entire estimation sample, regardless of sex and disability, then 81% of non-disabled males would be employed. In more opaque, but shorter terminology, you can say that the probability of employment for a non-disabled male, adjusted to the observed joint distribution of age and ethnicity, is 81%.

By the way, those numbers are not marginal effects. They are predictive margins.

[Anja Heimann]

That makes sense Clyde, Thank you!

[Weiwen Ng]

[QUOTE=Anja Heimann;n1597348]...

logit Employment c.age##c.age b1.Disability b1.Ethnicity b1.Sex b1.Disability#b1.Sex

margins b1.Disability#b1.Sex

.../QUOTE]

As an aside, since you know the basics of Stata's factor variable syntax for categorical variables, can we also get you to switch to the same syntax to automatically generate the squared term for age? If you use your original syntax with the manually generated squared term, then if you run margins at specified values of age, it won't calculate the squared term properly. If you use the bolded syntax above, margins will run correctly. Try it. It's magic.