Marginal Effects after Logit

[Kim Veloso]

Dear everyone,

I am trying to run a logit regression with a binary dependent variable and several categorical variables as independent variables.

logit y i.age_group i.sex i.educ_group i. marital_stat

age_group is divided into 5 groups (15-24; 25-34, 35-44, 45-54, 55 and above)
sex (1 male, 0 female)
educ_group is divided into 3 groups (no education to primary, secondary, college)
marital_stat is divided into 3 groups (single, married, divorced/widowed)

I am having trouble regarding the marginal effects and how I should be interpreting them. There seems to be so many ways of calculating them as well.

My first question is: Which type of marginal effects are considered optimal / more appropriate when all the independent variables in the logit regression are indicator/categorical variables - Marginal Effects at the Means (MEMs - margins, dydx(*) at means) or Average Marginal Effects (AMEs - margins, dydx(*) )?

I have read that MEMs might not be as good because it predicts marginal effects while keeping the independent variables at their mean values (for example the mean of sex==1 (male) is at 0.59 whereas the mean of sex==0 (female) is 0.41 - which is unrealistic). That being said, is it correct that AMEs are more appropriate when the independent variables are indicator/categorical variables?

My second question is related to estimating the probability that the outcome variable = 1 while setting the independent variables to specific values (following page 6 on: http://www.princeton.edu/~otorres/Margins.pdf ), and pertains to the command below:

margins age_group, at(sex==1 educ_group==3 marital_stat==1)

When I run this command, is Stata calculating the MEs/adjusted predictions for every age group, assuming that everyone in the sample has the following characteristics (sex==1 educ_group==3 marital_stat==1) i.e. forcing everyone in the sample to have these characteristics? Or is Stata calculating the MEs/adjusted predictions but only for the subset of people in the sample with these said characteristics? I hope I have managed to lay out my questions clearly despite my confusion on MEs; I would be happy to try and clarify myself further otherwise.

I would greatly appreciate any help. Thank you very much in advance!

[Phil Bromiley]

You'll increase your chances of a useful answer by following to FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex.

Whether marginal effects at the means or average marginal effects are better is really a substance question about what you want to generalize to. However, all of your explanatory variables are indicators so you are really estimating p's for different groups.

If you have any question, you can always specify more of the variables in the at statement or you can use the at option to calculate margins over a range of values for any of the variables. On your second question, Stata is doing a predicted probability for the different values of age_group at the specified values of the other variables. There is no forcing or averaging. It is taking the equation estimated by your logit and substituting in these values for the specified variables. If you don't specify a variable in the at(), Stata acts as if you set the value of that variable to its mean.

While you can do dydx margins, with logits it is sometimes more informative to look at predictive margins. You logit parameter estimates are already giving you probabilities versus the omitted category.